Checking your images on the little screen of your camera is known as chimping.
Though there isn’t really a pro and/or con there are some…
…advantages and disadvantages depending on what you are doing whilst chimping.
The first disadvantage could be that you are get too distracted from your shooting job if you chimp too much during a shoot.
The main reason for me to chimp is to control if I got my exposure spot-on. So I check my histogram when I changed my camera settings.
If the framing turned out to be bad or the main subject isn’t in focus I will delete the image on the spot. This prevents me from putting bad images on my computer that I would delete afterwards anyway.
There is of course the danger of deleting good images accidently.