Whenever it says I lag I just refresh the browser and it goes away. Hasn't been a huge bother for me but maybe it affects other people differently, perhaps based off of their location or their internet service provider.
Lag
I've experienced checkmating my opponent only to see it showed up on my screen, but didn't show on either the opponent's screen or the final scorecard. I, too, took a screenshot and posted it as a "comment" on the game because I was discouraged about it in the moment, but overall, I figure it all washes out. A handful of games over a few thousand isn't the end of the world. I feel your pain though.
Has anyone else noticed an alarming increase in lag on chess.com recently? I just played a game where I had played the winning move and then waited for 30 seconds, only for the Live Chess window to give a disconnect error. Then, when I get back, the checkmate position is on the board, but it says that I have lost on time. Please help me!