Paddy Wagon is a slur used to describe Irish in a derogatory way. Variation of "paddy." The term Paddy Wagon derives from the idea that the Irish were all criminals, and when the police came to quell a brawl or something of the like, they would just be rounding up a bunch of "paddys."
The word Paddy Wagon is a racial slur that has been used historically to degrade and dehumanize irish. The word is still used by some people for this purpose, and it is seen as offensive and hurtful to irish. If you are unsure about whether or not it is appropriate to use the word Paddy Wagon, it is best to err on the side of caution and avoid using it in any situation.