We will be using MX Toolbox, for our instructions. This is one of the best testing solutions out there. We have a paid account but the steps below are being done on the free (no account needed).
We start out at the homepage of MX Toolbox where you can type in your domain name (e.g. BusinessYETI.com) and then click on the MX Lookup button. The screen you will see will be similar to the below.
Not changing screens you will then see a link under the second box that says spf lookup. Click on this link. You will then get results similar to the table below. You should have all green checkboxes. If you do not there is somethign to look at. If you do not have an SPF record this will cause mail to reach users junk mail almost certainly if the email server you are sending to checks the SPF record (most do).
The above steps are the main steps for checking for mail server errors. We utilize the paid version of MX Toolbox which allows us to do 24x7 monitoring, blacklist monitoring, and mail server delivery.