Branagh pursued Lemmon for the part because he wanted a familiar face that American audiences identified with to open the film and bring them into the world he was creating. Branagh knew the language was a potential barrier for the American audience. Lemmon had never done any Shakespeare before and felt he never understood it, and was reluctant to take the job. Branagh wanted him anyway, and probably viewed the work through rose-colored glasses due to his interests. I imagine Lemmon was not happy about his performance, but as a rule, I don't think he watched himself on film.

EVERYONE has an accent.
Unless you're completely mute, it's impossible not to have an accent.

Lemmon doesn't have an accent and his so-called accent has nothing to do with why he stands out.
He stands out solely because his acting performance in this film is one of the worst of all-time.

Lemmon stands out as odd because he is performing with an American accent which Branagh would have encouraged him to do.
Its that man again!!

Some actors aren't good at Shakespeare. Jason Robard who is considered one of the greatest actors was terrible in a Julius Caesar movie. On the other hand, Charlton Heston, was a great Shakespeare actor.

So did I.

Please, excuse my English.

Where there's smoke, there's barbecue!

I can believe it.
I think the problem is that (a) he shows up right away, (b) it's a bit of a gleefully dubious sight Lemmon in antiquated soldier garb, complete with a tall hat, and his first few lines are the worst, and first impressions count.
"Farewell honest soldier and who hath releeeeved you."
It's all too much. You've just embarked upon a four hour screen version of the greatest play ever written, and there's one of the greatest screen actors delivering lines that somehow go over like a lead balloon.
In fact, it's kind of funny. Even looking at the subject line of this thread made me giggle a bit.
Branagh got a lot of things right in his film; casting Lemmon as Marcellus was not one of them.
But he does get better. Not immune to the odd clunker ("Shall I strike at it with my partisan?") but better.

The blu-ray edition of the film comes with a booklet that says Lemmon never did Shakespeare before Branagh's Hamlet.

You don't have bad taste. I, too, don't think he's as bad in his role as everyone says he is. Granted, he's not on par with most of the rest of the cast, but I thought he did all right with the role he was given. In the commentary on the DVD, Branagh himself defends Lemmon's performance, saying that Lemmon got undeserved criticism and that Branagh felt he brought gravity to the role of this old, down-to-earth guard.

I enjoyed him quite a bit, sorry to say. Maybe I have bad taste.

I'm rewatching this yet again, and yes, Lemmon isn't the right actor for Marcellus. I think he just wasn't used to the Shakespearean rhythm. Most of the British actors have done Shakespeare on stage.
"The pen is mightier than the sword, and is considerably easier to write with."Marty Feldman

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Who knows what happened? Maybe it was just an off couple of days for him.
I hate to admit it but when I watched his performance I had the feeling he spent the whole time worrying his dentures would fall out. I have no rational reason for this, it is just how it struck me. He seem so uncomfortable.
Ive lived upon the edge of chance for 20 years or more
Del Rios Song

Well he clearly didn't have dementia, as he continued to act to much acclaim right up to the end of his life, which was a mere four years away. Who knows what happened? Maybe it was just an off couple of days for him. Maybe he felt intimidated working in a Shakespearean production. Perhaps if Walter Matthau had been cast alongside him, he would have been livelier. But it's such a small part that his performance doesn't hurt the film at all.

Well, to be fair, if I cast Jack Lemmon in a part, I'd assume he'd be great or at least workable.

I have to agree. I love Lemmon, but he was totally miscast in this movie. Branagh likes to "stunt" cast like this (Keanu Reeves in Much Ado About Nothing is a good example) so people will start talking about the casting rather than the actual film.

I COMPLETELY agree. For a while I was like "Who IS that guy, and who did he sleep with to get into this film?" Then I realized it was Lemmon and I almost didn't believe it. At first I thought it was just his American accent, but then you get Billy Crystal (though I couldn't tell if he was doing the typical New York or attempting Cockney at times) and Robin Williams who still maintain some of their American lilt, and are stupendous. I'm not sure what was going on with him or really why they felt it necessary to include him, even though he's usually awesome.
Goonies (and neomaxizoomdweebies) never say die!