I suspect our network firewall is meddling with packets which is causing the md5sums to not match. Since I have zero control over the firewall, does anyone know of a program or download manager that would ensure the ISO downloads without issues?

kget also provides the md5..You can try it.
I am not getting your properly..firewall should not affect md5.
If your have further problem you can try SHA1....

Did you downloaded the ISO 100% completely ....

I've tried 4 different ISO files and they all result in the same behavior - md5sum does not match. I've even tried different browsers and the end result is the same. What do you mean by " Did you downloaded the ISO 100% completely ...."? What purpose would it serve to intentionally interrupt a download? Or am I missing another point you're trying to make perhaps?

how are you calculating md5sum ???
Did you tried verifying with sha1??

There is a free utility for Windows called md5sum. I saved the executable in my c:\Windows directory so that I could run it from the Windows shell aka DOS prompt. So, basically, md5sum /path/to/iso and the results never match the md5sum given from that particular mirror. I've done this several times in the past so I'm sure my syntax and procedure are sound. I've recently started working for another company with a new desktop and this desktop is the one I'm having problems with. I've also tried downloading an alternative md5sum tool for Windows and I'm met with the same symptoms. I tried with sha1 as you requested and it's unfortunately the same result. I just recently downloaded/installed a program for Windows called AccuHash and it shows the same output as the other free tools so I'm confident they're working as expected. I've even tried using other browsers to no avail.