I can't quite see what the weakness is? I am genuinely interested to know.
The mobile phone network is not secure. Probably secure enough for personal banking for most people though.
As I recall the GSM crypto is now easily crackable by anyone at all serious, or maybe Law Enforcement just have the keys?
Regarding the time thing. There is a widely used method for getting quite good time from the internet. NTP (Network time Protocol) takes account of network delays. (About 70ms London to New York round trip). If you are on DSL add several tens of ms to that. The thing is that not everybody bothers to use it. If it is turned on then vastly sub-second time synchronisation is possible. My understanding is that NTP is very clever about reducing the effects of network delays given a long enough synchronisation period. I though don't understand how it works.
For an internet clock go to timeanddate.com. Its clock will though I suppose lag the true time by the internet delay that you suffer.
If you want to play with NTP, one issue may be that the Windows NTP client was rubbish. It may be fixed now. Consider getting a different client.