This was something I considered very recently (when I realized my only remaining VGA monitor didn't support the oddball frequency put out by an old Supermicro server on which I was still running something important).
Some pros of laptop servers:
* Quiet.
* Low-ish power consumption.
* Doesn't take up much space.
* Built-in secure console.
* Built-in UPS.
Some cons:
* Limited in what drives you can put in it. Some laptops only support one drive, so you can't even do RAID mirroring. A real server will usually let you put at least a few high-capacity 3.5" drives in it, on SATA or better.
* Many laptops will overheat if run with the lid closed.
* If you get a burglary, a laptop is very likely to be stolen. (In a rack in a city apartment, I bolted down the servers with security head screws, and there was no way they were taking the whole cabinet, with a huge APC UPS anchoring it down.)