I'm convinced that the stereo and mono versions available of "Please Please Me" are actually different takes. The harmonica is different and one of the singers (I think it is John) sings a wrong word near the end of the stereo version. And the timing between each   speaker is a little off at the end of the stereo version.
Since "Please Please Me" is my favorite Beatles song, do you know if the various takes of the song are commercially available anywhere? I'd love to have them for my collection.

Yes, the stereo and mono are definitely different.
As for the other takes I don't know what you mean by 'commercially available'.

As it is I'm pretty sure nobody's ever heard the first slow 'Orbison' version of this song.

The difference between the mono and stereo versions was caused by an engineer using the wrong takes/edit pieces when creating a stereo version of the LP.

The main difference between the mono and stereo versions is as follows:
At 1:27 - John sings "Why do I never even try, girl", while Paul sings "I know you never even try, girl" - basically John sings the second line of the second verse not the third verse.

It sounds like John realises his mistake as he almost laughs his first "come on" line in the stereo version.

At 1:45 in the stereo version a harmonica edit piece is added at the end, but it is really badly done! The timing goes right out because the edit piece is slower than the left channel. It manages to catch up in time for the last chords though!

As far as I'm aware there are only 3 studio versions of the track (I assume that's what you meant by 'commercially available').

Mono - available on the mono Please Please Me LP and the CD re-release of the 1962 - 1966 'Red' Album

Stereo - available on the stereo Please Please Me LP and original copies of the 1962 - 1966 'Red' Album

Early take from 11th September 1962 - apparently with Andy White on drums. This version surfaced in 1994 in George Martin's collection and is only available on Anthology 1.