Migration would slow down many kinds of evolution. Lots of interesting evolution happens when you get divergence in island (literal or metaphorical) populations.
Migration does mean that any clearly beneficial changes will spread quickly, and a large population gives more chances for them to arise - lactase persistence is probably an example of this. So humanity probably does adapt quicker than it otherwise would to changes in the environment, if those changes affect most of humanity.
In the short term I'd expect to see humanity getting better at a lot of things as races intermingle and previously separate gene pools combine - a lot of things like height or fitness or intelligence seem to be combinations of many genes where "perfect" is in some sense the default; how good you are is a question of how many "bad" genes you've picked up (and most of the bad genes are recessive). I've seen anecdotal suggestion that mixed-race children are healthier (would be interested to hear if there's any proper studies of this). I suspect in the immediate term this will be a bigger effect than that of new mutant genes.
Migration does mean that any clearly beneficial changes will spread quickly, and a large population gives more chances for them to arise - lactase persistence is probably an example of this. So humanity probably does adapt quicker than it otherwise would to changes in the environment, if those changes affect most of humanity.
In the short term I'd expect to see humanity getting better at a lot of things as races intermingle and previously separate gene pools combine - a lot of things like height or fitness or intelligence seem to be combinations of many genes where "perfect" is in some sense the default; how good you are is a question of how many "bad" genes you've picked up (and most of the bad genes are recessive). I've seen anecdotal suggestion that mixed-race children are healthier (would be interested to hear if there's any proper studies of this). I suspect in the immediate term this will be a bigger effect than that of new mutant genes.