Can you post photos with a better view of what you're worried about? I'm guessing you're seeing some swelling in the particle board they use. It is something to be concerned about but might be in a location where it doesn't need immediate attention.
As to the question about moving a tank I use lots of buckets. I'll move everything out including sand. Set the tank up in a new stand. Depending on how grungy the sand is I'll use all, some or just a cup or so with new sand. I'll add about 10%-20% new saltwater and add everything back.
I've done this. Any poly bucket or best a rinsed Rubbermaid Brute garbage can is safe. Put all rock submerged in one bucket with aeration; put all livestock in another. With aeration and heat.er. Empty the tank down to the sand. That's a major part of the weight off. Try to engage as many strong friends as possible. If you have a new stand, put teflon glides under it. If you can position it permanently at this point, do. If not the glides will always help you move it, even years later. restore the rock. Start pumping the water back in. Restore corals. They can be out of water briefly. And as much WARMED new salt water as you can manage. It's safe to heat glass measuring cups of water in the microwave then pour into tank: this is water without life in it. Just get it up to temperature. BAG your fish. FLoat the bags. This will help cushion the fish against any temperature mismatch, and keep working on that temperature....once within 5 degrees, you're ok. Just keep adding water, aerating, until you have enough water to start your system up.
Move it? Repair it? Replace with new stand? What ever you decide to do, the suggestions already given is golden. But don't forget that you also have gear inside the stand that needs to be removed.
I am concerned about how this wood got wet in the first place. Splash over from the refuge? If you don't correct the issue now, you will be doing this again in the coming months or year if it is that bad.
Is it dangerous? As in....will my tank fall over? Probably not but the stand may flex enough to crack the bottom glass.
If you are replacing the stand with an exact model then I would not worry too much about doing the retrofit but if you are going to use a different stand, you will need to figure out the mechanics of getting your refuge tank and piping all hooked up to the main tank within short order of getting the lifestock back in.