This has resulted in him flipping over onto his stomach in his crib, and eventually sleeping this way almost 100% of the time. Even in the rare occasion that we swaddle him up (which we have gradually stopped doing over the past couple weeks), he will get his arms out immediately and flip over.
I know babies used to sleep this way ALL the time, but it is strange and a little uncomfortable to see him face down. I'm getting used to it though, and he sleeps SO WELL like this - don't we all? :)