If the tank penetrations are threaded holes I would be inclined to plug them with threaded plugs, it depends on how long term this smoker is going to be? If you are anything like the rest of us you'll be thinking about next time before you're done with this time.
Grandma always said "if ya can't be handsome ya better at least be handy"
To address the weak spots question......I would use either a screw plug or weld in a patch of the same material. Don't even consider weak spots as an issue.
Welcome to the crew, sorry I don't have anything else to offer. The tank looks fine, if you don't mind looking at some plugs that is the easiest for sure.
Making memories.
Current Smokers: Backyard RF Offset and Hybrid RF Offset trailer rig with Cowboy cooker and fish fryer, always room for more........