Might I suggest...
 

I've been ordering my inbox by using the tick boxes beside the individual emails and the "Mark" and "Move To" menus above. I wish that the functions could be coded so that after I make a selection (e.g. "Mark" > unread), the tick mark in the box beside that email would disappear so I could carry on performing other actions without inadvertently performing those new actions on emails whose previously-used tick boxes remain ticked even though their actions have been carried out.

While I understand where you're coming from, the problem with this suggestion is that it precludes you from doing anything else with those messages. What if you wanted to mark those messages as unread and mark them as pinned, for instance? Or move them to another folder after pinning them or marking them as read?

Granted, that might be an edge case for some people, but considering that it's pretty easy to quickly de-select all selected messages just by clicking on the checkbox in the column header (to the left of "All Mail"), it makes more sense to leave the messages selected and allow you to de-select them manually rather than forcing users who may want to perform multiple actions on a batch of messages to go through and re-select all of the same messages again.

My problem is not so much that it's difficult to undo the ticked boxes... more like it's difficult to REMEMBER to undo them and even more difficult to remember where they might have ended up because I forgot. :(

Well, at least they'll be unticked if you move the messages to another folder (unlike applying/removing labels in Gmail, which used to mess me up sometimes), so it's really only a problem if the messages are still in the folder you started in, and while I realize they could be way down from a scrolling perspective, the fact that you'll see "X Conversations Selected" at the top is a good clue.

So it's probably safer to just to make it into a habit of double-checking the header and then clicking the box at the top when you're done to ensure everything is unselected.

The alternative, which is unselecting them automatically, would be much worse for those users who want to do things like pin several messages and then move them to a folder — I know I'd have a harder time remembering which messages had been selected, not to mention tracking them down again in a long list :)

It is worthwhile to learn the main keyboard shortcuts, and train yourself to use them at appropriate times. I know that pressing"*" then "n" deselects all, and basically have a habit of using it after all actions involving message selections, unless I stop myself in time realizing I still want the selection. Occasionally (not often) I clear a selection I still want, but I cannot remember the last time I inadvertently used an old selection (in either FastMail or Gmail). It is nice that most shortcuts, where appropriate, are the same in the two mail clients.

That's also a good point. I often forget about that as I don't use the FastMail webmail client as often as I did with Gmail, where I had pretty much developed the exact same habit (*+n) regarding selected items.