I have noticed that not every successful trade appears on the Level 2 order book. Particularly for illiquid shares. Take the example below, where the book is filled with Market Makers. A lot of the successful trades made (Trades section) don't ever show on the book. My initial understanding is that the trades that never appear on the book are OTC orders and are only made "public" once they've actually been transacted, rather than the facilitators publicly disclosing their intentions prior to a deal being made. That said, I'm not 100% sure if (a) this is true or (b) if there are other types of orders that may never appear on the book but will appear as a successful trade.
There can be plenty of non-posted liquidity. So OTC orders that didn't match posted limit orders can occur, but so can trades between the posted spreads that just happened faster than the visual representation of the Level 2 will show.
The NBBO is 180 - 185 and someone sent an order for 183.75 and someone saw that order coming to the exchange - who also didn't previously have a limit order posted - and filled it instantly.