I asked the Toodledo team about this problem but, of course, it was just dismissed. The problem is not Blackberry's, as I am told. The responsibility lies with the people providing this service. At any rate, I would appreciate if any other users have had a similar problem, and if they were able to solve it.
The issue I am having has to do with syncing the time with the Z10 native calendar. It works like a charm: however, every task that I input online (i.e., through Toodledo) appears 5 hours too early on the calendar. In other words, if I set a task for 1 pm through Toodledo, it appears as 8 am on the Z10 calendar. The Z10 and online time zones are both set correctly, and no combination of changes to start/due date/time or event duration changes anything. So, online, I have set my Toodledo tasks 5 hours ahead. Note: the problem endures even if I 'artificially' change my timezone in account settings, or my Blackberry! Curiously, I am in the Eastern time zone, which is exactly 5 hours behind UTC ... not sure if that is related. Thanks in advance!