Advice on Furnace water leak, should I worry?
Water spilling out of a furnace is definitely a problem. As you've experienced, at the very least it may lead to soggy rugs/carpets and the ensuing mold. You also noted that there's rust and damage -- those also are not normal; they are signs that leakage is causing your furnace to literally desintegrate.
There are two common sources of water in a furnace. One is condensate from the exhaust; this occurs during heating season. When natural gas or propane burns one of the byproducts is water. It's a vapor as it leaves the burners but it condenses to liquid on the walls of the exhaust pipe and normally drains back into the furnace. The other source, if you have refrigeration-based air conditioning, is condensate on the evaporator coils. This is humidity that has been drawn/chilled out of the air.
Both liquids can cause problems, but it might be worth noting that the condensate from burned gas is somewhat acidic. That'll cause accelerated decay of the metal furnace cabinet.
So, what to do about the water? There should be some drainage tubes or pipes arranged to catch that water and carry it away, usually to a nearby floor drain. When there's water spilling out where it doesn't belong the first thing to check is that these drainage tubes and the catch basins that feed them are all connected properly and aren't blocked.
As for that loose band clamp around the coupling: it looks like an oversight. It should be snug. You wouldn't want furnace exhaust gases with carbon monoxide and other harmful substances leaking into your home through a loose fitting.