Admittedly, I've only seen one person espouse the extreme version of this view. They insisted that rather than eradicate a disease, we treat cubes in a city that had three cubes to prevent an outbreak, even though the card for that city was in the discard pile.
Eradication is very valuable, and is worth risking one outbreak, or even worth one certain outbreak.
On the other hand, eradication is an exciting, challenging achievement. It can be tempting to go for it, even though it's not the best thing for winning the game. You might eradicate a disease, only to have another area turn disastrous when an epidemic comes in a bad spot where a lot of nearby cities have two cubes.
The difference depends a lot on how far you are through the game. Eradicating early means you'll save a lot of actions you don't have to spend on treating that disease over the rest of the game. However, if there are only two epidemics left, and no city of that color has more than one cube, it's unlikely that color will ever cause you a problem again, even if you never treat it.
Thinking your role is your job
I've seen people who play the Operations Expert, and they immediately start off the first turn walking to Sao Paolo or Madrid or Tokyo and placing a lab. They continue to just walk around the board and place labs, at least until the board is nicely peppered with them. That's very helpful, but it's not the only thing you can be doing, and sometimes something else is more urgent. In fact on hard difficulty, something is almost always more urgent. Placing labs becomes a mostly tactical activity, with the lab having at least one specific use intended before the Operations Expert's next turn. I have even asked people to go treat cubes in a critical area, to have them reply that they're the Operations Expert - their job is building labs, not treating cubes.
Your role is not a job, it's an ability. Sometimes, your special ability is the best ability, but sometimes, one of the many abilities all the players share is the best move. People have to do different jobs.
The Scientist is usually the one to collect cards, but if he has one and someone else has four, perhaps he should give one instead.
The Researcher usually gives cards, but sometimes he uses them to make a lab or fly somewhere.
The Dispatcher often moves other people around, but if a city is about to outbreak badly on his turn, probably he should get himself there and treat it.
The thinking is at least partially correct for the Medic. The Medic is so powerful, that when possible, he should be positioned to treat two cities with as many cubes as possible, and should use cards as necessary to fly to treat if he's not near cities with a lot of cubes. However, if it happens that the Medic draws nearly enough cards to get a cure, he should still probably be the one to do the cure.
Treat before you leave
Pop quiz: If you are sitting on a city with two cubes, and two spaces away is a city with three cubes, what do you do?
A lot of people notice the danger and impulsively walk to the city with three cubes and treat two. That's not usually optimal. Instead you should treat one, walk to the other city, and treat one. Either way, you end up with one city with two cubes and one city with one cube. The difference is which city you are in. The right way, you end in the city with two cubes. That's better, because on your next turn, you might have an opportunity to treat one more. On the other hand, if you need to treat one more in the city you left, you will have to spend actions to return.
Leaving two cubes in a city might not seem so bad, but two cubes becomes three, and then an outbreak. An exception is if you have the Medic in the game. Then, it can make sense to leave two cubes, so the Medic can come clean both, or even clean three after another comes.
The rule is even more true when you fly between the cities. In that case, it might cost a lot of actions to get back. On the other hand, if the city you leave has a lab in it, you can sometimes ignore this rule. It is usually fairly easy to return to a city that has a lab, if you have an Operations Expert or the board otherwise has a decent lab network.
In general, some players make the mistake of doing the most important thing on their turn first. Instead you should plan all four of your actions before you take your first one.
Walking as your last action
This is more of a newbie mistake. Sometimes they will walk to a city with three cubes, planning to treat it next turn. On hard difficulty, it is likely that an epidemic will come before your next turn, so someone else will have to come treat the city before then anyway. Instead, you should stay flexible. End near to a city with three cubes.
An exception is the Medic. The Medic should often start on a city with three cubes, so they can treat that one and another highly infected one. Even if the epidemic comes and the city outbreaks, or even if another player comes and treats one cube, there is value in the Medic treating two or three cubes in one action.
Inexperienced Dispatchers commonly make a move that uses extra actions to achieve the same effect. Suppose another player is in London, and the Dispatcher wants to join them in Paris. The mistake is for the Dispatcher to jump to the player in London, then move both players to Paris, using three actions. Instead the Dispatcher can move the other player to Paris, then jump to him. That uses two actions. It's a simple thing, but some people miss it.
Even if you hadn't particularly intended to meet the other pawn somewhere, if you're using their pawn as a path to get somewhere, consider whether it's better for them to stay where they are or move to some other point on your path. It will cost the same number of actions either way. Sometimes they're best right where they are, other times it's better that they also end up where you're going.
At the start of a game with a Researcher, when everybody's in Atlanta, a lot of people look around and see who has the most cards of each color. Then they want those people to take the matching color cards from the Researcher (or for the Researcher to give them).
Where it can go wrong is if they're nowhere close to having five of that color. It's possible they go without drawing enough of that color for a long time, and have to discard cards. They might even get close to a different cure first, and have to discard the cards the Researcher passed them. That wastes cards and actions.
When the Dispatcher is also in the game, there's a much better option. The Dispatcher can always get any two pawns together with one action at any time. Just wait until the combined total cards for the Researcher and the other player are enough to cure, and then get them together. If the Dispatcher's turn is between the other player and the Researcher, however, you might want to speculatively get them together when the total is close, because the Researcher might draw the right color. If you wait, then it takes one more round to cure the disease.
If the Dispatcher is not in the game, then sometimes passing cards the first round in Atlanta is a good idea. If it gets you to one away from the cure, it probably is. Also, it's best if the player still has enough actions left to heal some cubes.
When they have the opportunity to use Resilient Population, some people look for the city with three cubes on the board that has the most connections. I am more likely to pick the one has the least. I look for the one that's most remote, hardest to get to, and not near anything else we want to go to. A lot of actions would be wasted going there, perhaps more than once over the course of the game. My favorite city for Resilient Population is Santiago, which has the fewest connections of any city on the board.
If you choose a city with a lot of connections, chances are there are adjacent infected cities. You will be there treating them at some point, and it will cost only a few more actions to treat the adjacent city. In addition, even if you make one of those cities resilient, you'll want to treat cubes in it. Otherwise there is the risk of a chain reaction if an adjacent city outbreaks.
A different type of use of Resilient Population is favored by some very good players. If two or more adjacent cities already have a lot of cubes, they might make one resilient to reduce the chances or number of chain reaction outbreaks. This is really an emergency measure, if you're not sure you can reach those cities in time to treat them to prevent the chain reaction. It also can be wise near the end of the game, when the considerations of having to return several times to a remote city don't apply.
Playing special cards too early
Some players play Resilient Population as soon as they draw it or as soon as they draw the infection card for a city they'd like to use it on. It never needs to be played before the epidemic strikes, unless you need to make room in your hand. The rules imply that you can play it after you draw the epidemic card, but before you reshuffle the discards. That gives you the maximum options for what city to target.
Some players play Government Grant as soon as they draw it, to place a lab in a region and a city they think it's strategically valuable in. Government Grant does need to be played until you plan to use some player action that makes use of the lab: either curing a disease or shuttling to some other lab. You can have in mind where you'd like to play it, but play it at the last minute. If you reevaluate your decision before that based on new information, you might avoid a mistake.
Don't Forecast unless the next player (or two) has some way to go treat some critical city. If the infection rate is at 3 or 4, and you play Forecast at the end of a player's turn before their infection phase, all the cubes will come by the end of the next player's turn. So unless that player can do something about it, rearranging the cards doesn't usually do much good. If the infection rate is at 2, then two following players can make an impact.
The same goes for One Quiet Night. If the next player can't treat critical cubes, the infections will have the same impact before or after their turn.