Longer games go by FIDE's "Laws of Chess" which has a section 7 called "Irregularities" that indeed specifies the behavior if you accidentally knock over pieces or the game board falls over or you make an illegal move (moving away a piece that was keeping you from check etc).

Resolving irregularities does require your opponent to notice the irregularity and bring it to the attention of the referee.

Not sure about Blitz.