En passant

When analysing a game it does not seem possible to apply the en passant rule for one's opponent which is confusing.

I have noticed this as well as it not automatically castling in analysis mode. You can get around it by dragging the offending pawn off the board.

I think the analysis board is like this to give you freedom to play anything you like - such as thinking "wouldn't it be nice if my knight on c3 was over on f5" and then put your knight on f5 and see how it works out. Then you go back and try to work out how to get your knight there.
Or maybe you try to come up with a plan by making several moves in a row, looking to see if this plan is any good, then go back and see what your opponent can do to stop this.
However, by giving you this freedom does mean it has to sacrifice implementing certain rules as it has no way to guess what you are actually intending to happen.

@wyndavies said
I have noticed this as well as it not automatically castling in analysis mode. You can get around it by dragging the offending pawn off the board.

I think the analysis board is like this to give you freedom to play anything you like - such as thinking "wouldn't it be nice if my knight on c3 was over on f5" and then put your knight on f5 and see how it works out. Then you ...[text shortened]... fice implementing certain rules as it has no way to guess what you are actually intending to happen.

You also have to castle manually but this is no great hardship.
I think the analyze board is a great feature.
Besides analyzing the current position and trying different things out, you can always reset the game to the start and see where the mistakes were that lost you the game.
I do this quire a lot!