Common new Olimar mistakes? All right, I can take a shot at that.
- Rolling to get around -
Rolling as an evasive action isn't necessarily bad (unless you're being super-predictable about it), but frequently rolling (like to get around) can get you punished. If you're having trouble staying onstage or maintaining stage control, this may be a contributing factor.
- Not spacing Fsmash -
Fsmash is a trap. It has a long-lasting hitbox that can outlast spotdodges/airdodges and can catch people running in. It can be somewhat safe if you're using it properly, but if you're hitting shields point-blank with it, you're going to get destroyed.
- Jabbing everything -
This one is probably just me, but I used to jab to cover everything and got punished a bit for it.
- Recovering improperly -
You have a few options for recovery, but you have to pay attention to what the opponent is doing. When you're knocked away and after you've finished momentum canceling, look for a purple in your line and use Uair or whistle to bring it to the front (if you have enough time). Purple toss is a useful tool for recovery (knocking them off the ledge, forcing them to evade/take a hit if they're coming out to gimp you, etc.) and you can still Uair them off the ledge if you need to. If a purple isn't available, look for a yellow. The larger hitbox means a slightly larger window to tap them off of the ledge with Uair.
Olimar has some good offensive options (aerials and pikmin toss) and defensive options (whistle, whistle bounce, airdodge, footstool) and you aren't restricted to using just one tactic to recover. It's quite common to mix whistle with an offensive option (like whistle to Nair). Fastfalling and immediately airdodging is also incredibly useful, but you need to be careful about doing that out over the edge. Like Hilt said, you should pay attention to when you use your double jump. Different people have different preferences, but many Olimars prefer to come up from below the opponent with a DJ Uair or hold a purple to throw from stage level to clear the ledge.
Sorry, I've forgotten where I was going with this. The point is that Olimar has some good tools for recovering, but you do have to actively think about what you're doing. If you do get smacked with something with some horizontal knockback (or low knockback, depending on where you are) after using your second jump, there is a good chance you're losing a stock.