I haven't worked with external emails providers. For now we are sending around 100-150k emails/day and we are using postfix as MTA.

Regarding server side rejects - again reading postfix logs can save you from such things. As an example recently we started seeing that we can't deliver a lot of emails to orange.fr, and the worst - if send just one email it always was accepted but when we sent bulk newsletter we had a lot of rejections - the reason was quite simple we've got rejected because of high frequency so we just had to throttle postfix on per domain basis.