@1974odaymariner20,
Welcome to the best sailing forum to be found anywhere. We all want to hear your story, and we all especially want to see plenty of pictures of your boat, and most especially we want pictures of you sailing her. So, everyone here will do what we can to help you get there.
KappyKaplan tagged me because I am the VP of Communications for the Mariner Class Association and am somewhat familiar with that boat. However, you are showing pictures of an O'Day 20, not a Mariner. It's nice to know what that extra foot in length and shorter cockpit can do for the cabin. That 20 looks very comfortable.
Just like the Mariner, as well as any trailerable centerboarder or swing keel boat, you want to check the CB for freedom in the trunk. Growth, damage, even swelling can cause a centerboard to get stuck in the trunk. Without sailing experience, you may not even notice your CB isn't lowered when you sail her.
The mast step and tabernacle, deck or cabin top under the step, the compression post that braces the mast below deck, can cause issues when old and inner wood core rots and becomes soft. Check for a depression around the mast base.
Turnbuckles get taken up to full closure as the mast sinks. Soft spots may become apparent as you walk around on the deck. In high traffic areas or areas taking a load, this could be a real problem. The rudder's pintles and gudgeons should be easy to work without slop.
Pay attention to the general repair and maintenance of the boat. A sloppy repair and poor, unseaman-like upkeep, by the owner is a strong indicator of the type of life the boat has had. Inspect every access point below deck. The presence of water isn't necessarily an issue, but it could mean there is an inconveniently hard to reach (difficult and expensive to fix) leak in the centerboard pin, the hull to deck seam, a thru-hull fitting, the mast step, the dead ports and hatches. Check if it is just rain from an open hatch, condensation or a leak.
There are a lot more things to look at, but these are common issues with used Mariners. Most problems are very fixable, however. It just depends on you and your abilities and time and, of course, money.
-Will