iMac won't recognise .MTS videos on my hard drive, how can I play them?
Try VideoLan. It is free and should handle most kinds of video formats.

The method for recognising AVCHD format is with regard to Apple Video applications, and not QuickTime. Those applications have the reader for that format. But you're only interested in viewing them so I suggested VideoLan.

Also there is a QuickTime plugin which recognises many formats, but I have never tried it with AVCHD or MTS formats. It is called Perian. Please note that it is no longer supported in the form of updates but it is still offered on the official site.