Last night I ran into this situation- my opponent had:

500 points, no character higher than 99.
GOTGM 102 Rocket Raccoon
GOTGM 101 Star-Lord
GOTG 003 Mantis (x3)
GOTG 005 Major Victory
GOTG 023 Yondu

The three Mantises were a major problem. They effectively turned Rocket into a machinegun nest as he was shooting 8 times on some turns. Star-Lord's once-per-game power Hadron Enforcer was used four times on one turn. Major Victory was double-TKing
people up then pulling them back. It was abusive.

My question is are there any limits to what friendly mind control can do? I know it can get extra uses of a once-per-game effect but does it also get around the "no using a free action to do the same power more than once per turn" thing? Does it ignore damage depletion modifiers?

I hate being caught off-guard because I'm unsure on a specific rule

It gets around multiple free actions, because the mind controller is the one giving the actions.
It does not get around the depletion modifier because it is still the controlled character making the attack.

Also based on the wording for star-lord I have a hard time understanding why your opponent would use it several times in one turn.

HADRON ENFORCER: Once per game, give Star-Lord a free action and choose an unoccupied square of clear terrain within range and line of fire. When you do, Star-Lord can use Pulse Wave this turn as if he occupied that square.

If you used it multiple times on one turn you still only get to pulsewave once and I would interpret it to be you can pulsewave from any of the squares that were picked, not all of the squares that were picked. I will let someone more excited about rules decide if that interpretation is correct.

Sorry the bit about starlord came out wrong. He used the remote pulse wave four times doing one damage to each character each time.

That is so awesome/broken..... depending on what side of the pulse wave you are on!

Its ruled as once per game, per mind controller. If you had 10 friendly mind controllers you could do 11 once per game effects. One from the original once per game figure and 10 more times because each mind controller also gets a once per game effect.

It's nasty... and perfectly legal.

I've done something similar with multiple Tony Starks (IIM), Cyborg (TT), Indigo (TT) and Lockjaw carrying Ultra Light Objects. Indigo uses Outsiders on Cyborg, Lockjaw drops off the ULO, and Cyborg blasts away.