The number one pitfall is that your server IPs are blacklisted (directly or by association). If you use the cheapest VPS providers they will mostly be completely blacklisted since spammers have previously used them.
We use our own email servers with our own IPs for automated emails (password resets, login tokens, welcome email, etc.) and MailChimp for newsletters. We have never had any real problem with Gmail or any other email provider.
We do see some of our clients having those problems, as far as we can tell, it is mostly caused by some sort of bad rating on IP blocks.
The number one pitfall is that your server IPs are blacklisted (directly or by association). If you use the cheapest VPS providers they will mostly be completely blacklisted since spammers have previously used them.