I have a feeling this is a REALLY stupid question.

Lets say I'm using Mint and I need to install a program via the SUDO command. I noticed that once this program installs and copies its files to say.... /home/Downloads ..... when I try to run the program as myself, it fails. Right clicking on the folder, I see the permissions belong to 'root'.....makes since because I used SUDO to install it?! If I use 'sudo chown etc' to change ownership of that folder and its sub-directories back to my account, I can run it perfectly.

Is this something I'll need to just remember to do every time I need elevated access to install something or am I not using the 'sudo' command right?

That really depends on what you install, most programs grant system-wide user permissions when installed. Mint uses apt, Synaptic is an apt GUI, but is only run as root (or sudo, I hate sudo, I use "su" whenever possible), whenever you install pretty much anything from the distro's repo, it will appear in the menu, ready for any user to use, unless it's a tiny binary that has no GUI, then it's run from the command-line (depending on the type of binary, you may have to run some non-GUI progs as root as well). You'll notice programs like Bleachbit or luckyBackup have to separate icons, one is regular user, the other is root activated, that's because they are both file-system progs that sometimes require a higher level of system access. I hope that's not too confusing. So I guess the answer to your question is yes, if you are installing special things by hand, you will have to manipulate their permissions from time to time.

Edited for spelling and grammar.

it seems you are confusing "downloading" with "installing".

you don't need super user privileges to download something to your /home/<username>/Downloads (i hope you didn't really use /home/Downloads???).

there are some fundamental differences in how linux managaes software installations, compared to windows.
please show us what, and how you "installed".

You should download to /home/user_name/Downloads and not sudo until you actually install the program with make install, or some like command. If your installing from a package manager you don't need to worry. If your using /home/Downloads, you had to be sudoed to make the directory. So, you won't be able to expand and untar source packages as a normal user in that directory. If you want to do it that way, you must chown -R user: /home/downloads, and then not use sudo to work in that directory.