1. Continuing to fire at an enemy.
Even if that enemy is not firing back, continuing to fire at a target early in the game can become a problem.
Early in the game, if you have a line of sight to an enemy unit, there is a good chance that many of the enemy can see you too. Why this is a mistake (again, at the start of a match) is that while you hit one guy with everything you've got, you are then spotted by his teammates and they fire at you with more 'mechs worth of firepower. It doesn't seem like a mistake because most pilots then back out of view and think because they are still alive, they did a good job.
The solution is to fire one salvo and then duck out of view until the match plays out where you KNOW where your enemies are and who can see you.
2. Waiting until you overheat to deal with heat.
Similar to 1, waiting until your 'mech shuts down makes you a lot more vulnerable than you might think, and because a novice player often mashes override and still walks around after it, he doesn't register it as a mistake.
There are exceptions to this, but in general, when you your heat starts getting to about 60%, you should take a break. Try to maneuver to better position, or just take a moment in the match to see where everyone else is and what they are doing.
3. Chasing the light.
Even though the spider that popped over the hill is now running from with a missing arm, continuing to focus on him can have hidden costs. If that enemy has any sort of experience he will be doing two things: turning your attention away from the enemy, or luring you to them.
Chasing the light has the hidden cost of a) allowing the enemy to reposition (such as crossing open fields where you had a better chance of shooting them) or
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Lights SHOULD be delt with, but most of the time, particularly early in the game, they should be brushed off, not chased. Fire a few salvos to get them to move, leave chasing lights to other lightweight members of your group, and focus on monitoring the bulk of the enemy.
4. Waiting until the LRMs are incoming before doing anything about it.
The novice pilot starts a match, moving forward looking for enemies. He doesn't see any, so he continues moving forward, walking across an open field. Halfway across this field, the warning comes up "Incoming Missiles". For an agonizing full minute, the poor novice pilot turns to the nearest building and starts running, all the while three 'No skill cowards' are pelting him from afar with about 100 missiles total. Enough of them land and the Novice pilot is dead. He screams about 'game balance' then disconnects. Sound familiar?
LRMs are something that are best PREVENTED rather than cured. Like fire exits in real life, starting a match should always have in mind "where is my cover" and "where am I visible". Even though you do not see the enemy, you should move as though you ARE seen, and travel from cover to cover. When you DO receive missile fire, and you do reach cover, stay there a little while after the warning to wait for their lock to expire.