The apostrophe, again?

BBC4 started a new series about the quirks and idiosyncracies of the English language tonight, and with no hint of a surprise, the apostrophe featured in one of the first quandaries for the panel.

I'm wondering if their answer was right, but I admit the point that was raised isn't one I'd come across before, so I just don't know.

The reference was to the dotting of is and crossing of ts. According to the question-master, the correct format is to refer to the dotting of I's and the crossing of T's.

My problems:

• Capital I doesn't have a dot.
• The I's and T's are plurals aren't they? That means no apostrophe. 
• But the I's and T's might be possessive of the dots and crosses, so the apostrophe is correct.
• is and ts look terrible – I's and T's just look right.

Well, thinking about it hasn't helped, but I guess I'll just be going with the flow as it's the most readable and understandable.