Hey folks, tonight I replaced the alternator on my 2005 Ford Five Hundred (WHAT A PITA!!!!) and everything went well except for when I mistakenly loosened the nut on my tensioner pulley but once I realized my mistake I tightened it back down. My car is back up and running, tested the battery with a multimeter and everything is working great except for a new higher pitched "whirring" or whining sound coming from near the alternator / tensioner pulley. Should this be a concern and what is my path moving forward?

Here's a video of the sound: https://streamable.com/78xi63

 

would be a concern to me, as it is obviously to you. Get to Harbor Freight and get a Mechanics Stethescope (<$10) which will help you ID the exact source (I'd then replace that part). In the mean time I'd continue to drive it for a week or three, if you don't have a good alternate vehicle. Welcome to forum.

 

It is common practice to replace the tensioner when replacing the belt or other components.
Sometimes you can do the same thing with a long handled screwdriver or piece of dowel stick placed close to your ear and moved from one area to another. Depending on where you purchased the alt, it could be coming from there.
You must be very careful placing any kind of object near moving parts !!