So I noticed today there's some rust spots showing up on the outside/bottom on the water heater. No more than a couple specs. Should I be worried?
Most water heaters have an inner tank surrounded by an insulation material surrounded by the outer shell. If it is the outer shell that has some rust spots then there probably is not anything to be worried about. So depending on where the rust spots are located you may not need to worry about them at all.
But considering that you are seeing rust spots on your water heater that might mean that it is fairly old. If it is old, then you should think about replacing your water heater... a new water heater will save you a lot of money in energy costs (new ones are much more energy efficient).
Water heaters have a sacrificial rod in them -- sometimes two -- and the rod will sacrifice itself to protect the tank. This rod is supposed to be replaced every 6 years or so. If there are two rods, then probably every 10-12 years.
If the water heater is under 5 years old, or if you've been replacing the rods, then there shouldn't be any problem unless the water heater is 20+ years old.
If you haven't been replacing the rods (and are long past-due), or if the water heater is old, replacement might be necessary.
Sounds like the inner tank is potentially leaking, and leaving the outer jacket wet. Ever see what happens when a hot water heater fails? It can be catastrophic, tearing through walls and floors, or just get your floor wet. Either way, you may want to get it checked out.