Beverly Hills Cop looked good on standard DVD in 2002, when a special edition was released. On Blu-ray it looks considerably better, though without question the film shows its age. Especially evident is the graininess of the entire presentation. It's simply the look that many films of the era had, though it becomes amplified when displayed in 1080p high definition. The darker interior scenes are much more grainy, while daylight exteriors look very crisp. Detail is relatively strong overall. The colors are kind of drab, but again this is likely an accurate representation of the original cinematography. The movie hasn't looked better on a home video format.
The DTS-HD Master Audio 5.1 mix is utterly unspectacular, without there being anything in particular to fault. Dialogue is easily intelligible and free of distortion. But don't expect much out of the surround sound experience. The front channels are where the vast majority of the audio is heard. Rear channels are very rarely used. The LFE channel is surprisingly not very active either. Bass is present, but generally thin. The famous "Axel F" theme, along with the rest of the hits-laden soundtrack, is similarly lacking in real presence. Overall the audio presentation was very similar to the 2002 standard DVD edition.
Speaking of the 2002 edition, that release is the source of all the supplemental material found on the Blu-ray. Director Martin Brest's audio commentary is ported over, along with around 50 minutes worth of standard definition featurettes. The best of these is the half-hour "The Phenomena Begins," which provides a good overview of the entire production. If you already own Beverly Hills Cop on DVD, I can't really find reason to recommend the upgrade.