I'm not enjoying season two as much as season one

I think you're taking it way too seriously. If you look at the "I, Mudd" and "Trouble with Tribbles" episodes as comedies, they work a lot better as Star Trek stories. You want a shitty episode, "Who Mourns for Adonis?" "Catspaw," "The Apple," and "Assignment Earth" are all real stinkers. However, the absolute WORST episode in the entire series, in my opinion, is "The Alternative Factor." Every worst trope, terrible story-writing, and shitty special-effects all wrapped up in one episode.

Lots of classic eps in s2 and just a few stinkers. , only a few classics in s3, lots of stinkers

I did a rewatch a few years ago and I felt S1 & S2 were about the same. I didn't have any issues with the comedic elements. One of my favorite episodes, 'A Piece of the Action,' is in Season 2, and that has a good bit of comedy in it. Another favorite of mine, 'City on the Edge of Forever,' is in Season 1, which does have a more serious tone, so I think your observation is accurate. Regardless, I liked most of the comedy injected in Season 2.

I honestly can't remember anything from Season 3, other than 'Spock's Brain,' which is pretty bad. S3 is still worth a watch, though.

A few turkeys, sure. But S2 had some of the best episodes.

I, Mudd is indeed a stinker, but the Tribble episode isn't bad because the "humor" isn't intentional (I don't think I'm getting that point across), but with I, Mudd, the whole pointing with the "finger guns" and whistling to confuse the android was just stupid. Roger Carmel's acting was borderline over the top in the first episode but just under so it worked in contrast to Kirk's seriousness of the potential of losing the Enterprise to destruction. In I, Mudd, Carmel was just obnoxious over the top.

I liked most of the shows.

You may not have liked Mudd but he's an instantly recognizable to fans and I think he was only on two episodes.

I believe he's a character on the current Star Trek show.

A great way to enjoy older programs and movies is to imagine you are seeing them when they came out. There was nothing like Star Trek so the episodes were amazing, exciting, and different for people who liked that genre.

Also, the acting on the show is really excellent as is the dialogue.

I have watched all of the different Star Trek shows and they have bizarrely bland acting compared to the original series. Again, if you imagine being in the situation they are, being on a ship totally alone, and they keep encountering one threat after another that is frequently mindboggling then Shatner acts appropriately as Kirk. The dialogue and acting for Spock has never been equaled.

I have enjoyed rewatching for the stories but more so for the characters.

S2 is definitely not as strong story-wise but I think it's better character-wise, the actors have grown into their parts and the writers have more of a feel of how to write the characters. S3 is definitely a big drop off.