I've totally taken apart my first (and most used) 10/22 countless number of times. Most of the pins fall out by just tipping the receiver over. Just normal wear and tear from being removed and re-inserted. IMO, nothing to worry about. The only pin that doesn't fall out is the one holding the aftermarket plastic extended mag release. The release seems to hold the pin tightly.
Just curious, when you had the bolt held back after the last round, did it stay back when you removed the mag from the receiver? Was this gun bought new or used? (The 10/22 was not designed with a bolt hold open device actuated by an empty mag. Have never seem a factory or built up 10/22 that held the bolt back on an empty mag.)