I guess they had guys wearing dresses in Korea since Klinger remained on the show.

They dropped Spearchucker either because they found out there were no African-American surgeons actually present in a MASH during the Korean War (official reason) or else they were trying to pare down the number of characters.

I've only seen the movie a couple times and it has been over 30 years since I saw it. But I seem to remember that Duke was more of the lead and Hawkeye was the sidekick, with Trapper being a bit of an oddball. I guess in a TV show you can't have everyone so they decided to drop Duke.
Obviously the Captain Forrest mentioned on TV was not the character from the movie as we never actually saw him or ever heard another mention of. But I think it was just a little subtle joke the writers threw in.
I do wonder why they had characters like Spearchucker and Ugly John around and just drop them after a few episodes.

A reference, sure, but I don't think it was the same character.

I always thought the name was a reference to the Duke character from the movie.

It is a coincidence. Why would they refer to a friend as Captain Forrest and not Duke Forrest?
Exactly, and besides, Forrest is a relatively common name.
Maybe they excluded Duke from the series because they only wanted two protagonists to focus on: Hawkeye and Trapper. Pretty ironic, since Trapper was stripped of credentials and shoved to side almost instantly.

It is a coincidence. Why would they refer to a friend as Captain Forrest and not Duke Forrest?

Duke was mentioned once in the show. Hawkeye and Trapper talked about a Captain Forrest and said he went back home to open a toy store.
I'm still not convinced that Duke and "Captain Forrest" are the same character. It could be a coincidence, or they just borrowed his name.

Duke was mentioned once in the show. Hawkeye and Trapper talked about a Captain Forrest and said he went back home to open a toy store.

So were Spearchucker and Gen. Wood.

Ho Jon, Ugly John, and Lt. Dish were in early episodes of the TV series.

There were a lot of characters from the film or book that were either dropped or not used
Dropped
painless pole
Spearchucker
Ho Jon
Ugly Jon
General Wood
Duke
Cpl Judson
Lt Dish
Capt Macarthy

After Hawkeye and Trapper returned from Japan, Duke was sneaking Hot Lips out of the Swamp.

Duke banged Hot Lips while Trapper and Hawkeye were hanging out.
Really? I don't remember Duke and Hotlips getting it on.

I think the remark about sharing with yankees is a joke rather than a complaint. Duke appears to fit in quite well with the other two in the film.

No, Trapper was the single one, Hawkeye was married with kids.

We do see Duke in the movies get his orders to go home, in his final scene while helping Spearchucker with a tricky brain operation. There's a flash-forward shot of him on the tarmac embracing his family with a huge grin. He's the only character in the film and series who gets to do that for us to see.
Maybe that was the one moment they didn't want to play with? I agree with Revolver about his character more or less being folded into Trapper's for the TV show. Was Trapper a family man in the movie, like he was on the TV show?

It was established in the film that Trapper and Hawkeye had a history. They also shared an interest in golf and had their adventure in Tokyo. Despite coming and leaving with Hawkeye, Duke never really connected with him. Duke banged Hot Lips while Trapper and Hawkeye were hanging out. He complained about sharing a tent with the two yankees. The whole shower scene was set up based on a bet between Hawk and Duke. So there was more of an opposition than a partnership.
Also, very early in the pilot, there is a scene where Hawkeye and Trapper go against Hot Lips and Frank. It's an even two against two. With Duke and Trapper, it would look like three people ganging up on the two majors.
Lastly, just as Major Hobson and Frank Burns from the book were combined into one character in the film, I always thought the curly-haired Trapper and Southern Duke were combined to form Wayne Rogers in the serious.

I'm not sure of why Duke wasn't written into the script. My guess would be he was too conservative for the tv conception, but Tom Skerritt was offered (and turned down) the role, so I'm probably wrong. Most likely, like so many of the other characters brought over for the pilot and early shows, he would've been written out shortly anyway.