Windows Mobile 5.0 or above is fine, as long as Excel is installed.
I'll be honest, although Round Tracker is usable on a hand held device, I personally am more inclined to just print off the work list for the day and take that with me to refer to.
When I'm out cleaning 'time is money' and I find it quicker to update the sheet with a pen (You can remember what you've done anyway so you only need to do it every now and again if at all. It's more of a reminder of what's due or to give to other lads as a work list).
Round Tracker is designed to be really quick to update multiple info without having to navigating through different screens so it only takes a couple of minutes when I get back home to update it on the computer and print off tomorrows work list.
To me, using a hand held device to update jobs or check what's due when you are out cleaning is too 'faffy' compared to a pen and paper, whatever the program.
Having said that, if you have Documents to Go installed and keep your Round Tracker file backed up on a SD card which you use in your device, then it is very handy for making appointments, as you can see at a glance which are your quiet days on any given future date and book a job in very easily.
Hope that helps.