If my opponent makes an illegal move and then hits the timer, is there any kind of penalty? Doing so is significant blunder during a speed game.
Yes, there could be a penalty. Some players may choose to let this type of mistake pass. But in all other cases you need to stop the clock and go get a TD. Depending on the ruling of the TD, you could have some time added to your clock.
In a speed game, this could even result in the loss of the game. I always have that rule announced well in advance for my blitz tournaments.
Alex Relyea
If it is just a game between two friends, just hit his clock and tell your friend to make a legal move. If you play countless games with your friend, you are going to perform the same error down the road.
If it is a non-rated USCF event, the norms of the local players will be the final judge how they want the penalty performed. If there is no established norms, the director will over time set the norms of blitz rules. Each local area is different how they perform the penalty. Some you lose the game, others you must make a legal move without the loss of game or time adjustment. If your opponent made the illegal move, if the King can be captured, capture the King as that ends that. If there is a variation on that, never been to one.
3. Illegal move penalty. A player who makes an illegal move in Blitz and presses the clock does not forfeit. Instead, two minutes are added to the opponent’s remaining time.
Variation 3A. Illegal move cause loss. A player making an illegal move and hitting the clock shall forfeit the game, if called by the opponent before touching a piece. The one exception to the touch restriction is if a player leaves the king in check, the opponent may then touch the piece delivering the check and remove the player’s king from the board in order to claim a win caused by such an illegal move.
As a personal note, like variation 3A much better. Not all directors or players like the USCF blitz rules. That is a different story! 
Yes I like 3a as well but 3 is an acceptable solution as well. I didn’t have my rule book here with me at work so thanks for the answer.