I think its your experience level, the aircraft and your ability which determines what are your warning pointers when looking at weather from anything from non aviation forecasts to TAFS METARS etc or good old instincts knowledge and the mark one eyeball.
I know with my own flying there are specific NO NOs but they are short
If there are strong winds forecast you look into those in more detail, wind direction runway etc even terrain for turbulence shear.
Fog at destination is the main show stopper so you then look at fuel alternatives etc
In non deiced/anti ice aircraft, cloud base freezing levels etc
Always specific warning pointers
Pace