Reputation is one of the most important things when having your own mail server. Providers have no trouble blacklisting you because of emails potentially containing spam, or even when sending a lot of emails is one of the reasons to get blocked.
To help you build your reputation, here's a list of tools you can use to test your current deliverability score:
When you do have the suspicion of emails not getting delivered, it is good to check the blacklists. Here's a list of the most common checkers.