You're not alone, I've been experiencing the same thing. I made sure the graphics card driver was updated yesterday, but I've still been experiencing numerous problems since the latest patch.
I'm currently using a 'gaming' laptop with an Nvidia 580M graphics card. While I can't say the laptop itself has been error free, I haven't experienced any STO-related specific issues, and I've been playing STO on this rig since May of last year.
I had several BSoDs as well, but I'm very certain it was due to my rosewill card reader malfunctioning, I took it out last night and so far I've been bsod free, be sure to double check your hardware and drivers...