...how realistic is it?

I don't think any TV show is realistic. In Barney Miller's case, I don't think detectives would be sent to stop crimes in process. They'd send uniformed cops in the closest car to the crime.

It is sometimes said that Barney Miller is the most realistic cop show. I think that's because it's shown as a regular job with people doing paperwork, struggling to get in on time, etc., and because the perps are mostly presented as unbalanced rather than truly dangerous.