A young couple in a car exactly like Starsky's is killed by hitmen and word is out on the street that there's a contract out on Starsky and Hutch. This is a TV-pilot that was an ABC Movie of the Week and later turned into the TV-series.
Starsky gets drunk from having too much moonshine (S4E5). There is no visual on him getting sick as he does it behind his car. He is seen covering his mouth beforehand. I don’t recall there being any audio on it, and if there was, it was not very noticeable. I don’t have the exact time it happens in the episode, sorry. It’s after Hutch gets Starsky into the Torino and I think they almost crash/run into someone because the car is stopped in the scene where Starsky gets sick. It’s a very brief scene and it’s more of a background thing anyway as Hutch is responding to something over the police radio while it’s happening.
I’ll put this up as a warning just in case. Hutch frequently talks about/demonstrates “healthy eating” (he comments on Starsky’s less-than-healthy eating habits as well) He also mentions fasting as I recall he does something like a 48-hour fast. Either way, he’s quite focused on “health”. It’s not clear whether he actually has an eating disorder or not, but it can be perceived as such.
A major addiction episode is “The Fix” (S1E5), where Hutch is kidnapped, forcibly injected with heroin, then is forced to withdraw so the bad guys can get information from him that they want.