If you don't tow often, double-check the registration on the plate.
Inspect Trailer Tie-Down Locking Mechanism, and Materials. You're looking for cranks that physically won't turn (due to rust), worn straps due to friction or chafing, or broken hooks or loops on the object being towed.
Are your wheels self-greasing? Do they need fresh grease injected every so often?
You mentioned tire pressure; don't forget tire tread and overall tire life. Any dry rot should warrant immediate replacement. Nothing like heading down a 6-lane expressway on a loop around a major city and feeling an immediate drag as you look in the mirror and see a massive puff of smoke (not that this ever happened to me...)
Don't forget about proper load distribution on the trailer. If you look at the videos on the Internet where a trailer on the highway starts turning right and left and ends up jackknifing, it's usually because the load was placed too far back on the trailer, causing it to lift up in front.