I have a simple enough algorithm.
Is it on the CW? If so there had better be some serious evidence that it is good (probably the last thing to have this happen would be Reaper).
Is it a comedy show? Same again, the last it would have happened for is probably Legit but I had seen all his standup before so it seemed to be covering the same ground (it was intended to but hey).
Do I already have a bad medical show on the go? If so then I do not need another. Basically all medical shows are bad medical shows by the way, you probably get a great comedy more often than you get a good medical show.
Does the plot basically reset every week or is there an actual attempt at a longer form plot? If the former then ignore it. Many screenwriters now seem onboard with long form TV which is an awesome development, I am not sure what to thank for this.
Is it a crime show? Are we still living in a post wire world? If yes then you can probably ignore it. For further questions is the show built around a central gimmick where the main person has a strange ability? If so then you can probably ignore it or just watch the pretender again, minor exception if the gimmick is actually supernatural. Definite miss if the premise is "just an old fashioned lawman in a modern world" or some minor spin on the same, NCIS does not count in this but something like The Closer would.
Related to the definite miss above, if the main character is put forth as a paragon of virtue for which the marquis of Queensbury provided a true way of life/fighting then definite miss.
Also related to the above. Do the writers seem like they would like to be back in fantasy 1950's America? Ignore the show as hard as you can. This does include things like Mad Men and even stuff like suits which kind of stems from it.
Am I likely to learn something by watching? Definitely an option, Burn Notice and Lie to Me are good examples.
Is it on the discovery channel or something similar? Ignore it until I am bored and they are playing a marathon one weekend.
Reading the comments on the show. Is a big draw that there is a very pretty person running around with not many clothes a lot. Do you have a functioning internet connection? [probably as broadcast TV is far inferior to computer delivered TV] Then it does not matter and you are probably too desensitised anyway. It can be good in spite of that though, Graceland and The Blacklist being two exceptions in recent memory.
Is J.J. Abrams involved? This is good but bail out before they let him have free reign and you start getting supernatural or truly crazy conspiracy nonsense, doubly so if the plot of the original series has been resolved (resolved can also mean "well these uber bads were just revealed to be puppets for an even bigger bad).
Someone somewhere said something about amnesia, it truly is a hack's device in screenwriting and a red flag as a result. It is not necessarily fatal though.
It varies slightly for non US TV (the strict season model and need for some 20 odd shows per series damages things a lot for me) but not by an awful lot.
I would also have "magic computer"/"that is really not how a computer works" in there but that would mean I have nothing at all to watch, probably not even Game of Thrones.
Edit. Forgot to add. If the show is about con artists and is even close to bearable I will probably watch it. There have not been so many bad ones in recent years though, granted there have not been many at all in recent years but I can hope for that elsewhere.