There certainly are risks with any repair you carry out on a phone.
But, you're on this site for a reason!
Here's a list of things that could happen:
- Logic board damage, from prying up connectors incorrectly.
- Slipping with a screw driver and knocking capacitors off.
- Piercing the battery, causing it to burst in to flames.
- Putting screws in the wrong place and causing damage to the logic board, by crushing traces in the logic board.
- Blowing the backlight on your phone, by not unplugging the battery first, before you remove the screen connectors or reconnect them.
New batteries don't tend to cause damage to your phone, the only thing that can happen is a faulty battery.
If you have any other questions let me know. :-)