In supplying electrical power to an AP (either 1252 or 1140), does a power injector have any advantage over a local power supply -- other than the electrical outlet does not need to be nearby? Does the power injector have any disadvantages when compared to a local power supply?
Right, the primary advantage is that a power outlet is not required next to every AP. You can also turn off an AP by shutting down the switchport, you can have flexibility in moving APs around, etc...
As far as AP functionality is concerned, there are no advantages/disadvantages to using either one. Both provide full power to the AP.