InDesign selects a line or a paragraph whenever you triple- or quadruple-click text (you can set this feature in the "Preferences -> Type" dialog box). To highlight a single letter or an arbitrary fragment of text, you have to click and drag. Maybe your mouse is multiple-clicking when you're trying to drag text.
I have been using Indesign since it came out. So I'm pretty familiar with it.
Actually it is not a clicking problem. Even if I just click between letters the whole line will highlight. Also get the same result when I place the cursor by a letter and use the arrow key right or left not using the mouse.
We have been having problems with both Macs recently and have come up with a work around.
We saved the files back to IDML. We are currently using CS6.
It seems to be an issue with some older files that aren't playing well with CS6. Probably due to plugins that were there in older versions and may be missing in the newer version but not sure.
If exporting to IDML solved the problem, it was indeed a case of corrupted file, caused by one of the issues you mentioned.
Recently I was having some headaches with the zooming function of InDesign. Eventually I found out it was simply a matter of changing the almost dried batteries of my wireless mouse :-) That's why I suggested that your case could be a hardware problem.