There were no bugs I stumbled upon. All trophies popped up as they should, just make sure you install the latest patch.
The game just has performance issues (FPS drop) on some parts, still very playable though.
You're right about the not carrying over the stars between on/offline mode.
IIRC I did it offline, either way it should work though. Some guides also say that all the trophies (including DLC) can be earned offline, so there's that.
- Beat Zico: HD Equal or beat the lap time of 30.82 seconds on Anulpha Pass (Forward), Speed Lap, Venom, using the Piranha
After many attempts (2+ hours),
I managed to get 30.79, thanks to this video guide