Local real estate values will guide the decision. If you're in a high-value downtown area, certainly it can make financial sense, i.e., a higher return than leaving things as is. And even "as is", the smell of mould throughout your living space is not only a financial detriment but a health hazard.

Having seen so much shoddy "waterproofing" over the decades, my main concern is that it be done in what is the right way in virtually all situations: from the exterior.

That’s an interesting point. I was wondering whether an external french drain, proper downspouts, repointing of the foundation, etc were a better way to go.

External weepers require excavation. When the foundation is exposed, it can be waterproofed in a variety of ways.

repointing foundation

only if it's brick or block. A rubble foundation cannot usually be waterproofed from the outside. It tends to fall down!

Can you share the cost with the other owner?

Yes, but since they are on the second floor and have access to attic space for storage, they don’t have much incentive to put money into fixing the basement. I, on the other hand, have direct access to the basement from my unit and can smell the mustiness. I also have no storage without the basement.

"partial concrete floor"? Does that mean you have some dirt floor? Dirt floors can let a lot of moisture through. See what laying 6 mil polyethylene over the whole floor does to the humidity and mustiness.

Yes I think I have some dirt floor. I will give that a try.

What kind of dehumidifier do you have? If it's a cheap onr from sears/home depot, you obviously need something better. The builder quality dehumidifier systems should work for you (around $3000-$5000). If it is a large builder quality unit then it should not be freezing up if its working properly and your basement is the typical 50-60 degrees. Have you had it serviced/checked out?

It’s a home depot one that can only dehumidify like 800 sq feet or less. I put up plastic sheeting around an alcove/small area in the basement with some of my things and stuck the dehumidifier in there. (This wasn’t a long term solution—just an experiment to see if I could protect some of my things.) As I understand it, the dehumidifier is similar to an air conditioner in that it pulls moist air in, exposes it to cold coils, and then the water drains off (into a bucket). Well the combination of the cold air in the basement and the cold coils has caused ice to form on the coils stopping the whole dehumidification process. Side note: it definitely dips below 50 degrees in the basement.

"Yes I think I have some dirt floor"

First thing to determine is if you truly have a dirt floor. Because if you do until you cover that up you are peeing in the wind for the most part.

The attic is there “exclusive use” space, but the roof is common, so if the roof were to leak, we would both have to pay to fix it or our master insurance would cover it. The basement is pure common area. Both of us store things down there and our water heaters are down there. My washer and dryer are down there as well. Water is a common expense. The electric... ugh.... don’t get me started. When the building was converted from a single family to a 2-flat, the contractor didn’t really separate the electric. Consequently some things in my unit are on the other guys circuit and vise versa. Basically the upstairs folks have to split the expense if anything done to the basement unless I want to change the master deed so that all of the basement belongs to my unit. Even then, they’d still need to be able to get into the basement to access some mechanicals.

I do need to do some exploration of the basement floor. If it is all concrete, there are definitely major sections of it covered in dirt.

I any event, it sounds like you need to cover the entire basement floor with plastic and tape the seams. Look at the specifications of your humidifier, it should say its operating temperature range. Most go down to 40 degrees.

After you figure out what kind of floor and foundation you have, and have read your condo documents, it might be worth your while to have an inspector (a certified one, not a glorified handyman) come in to see what could be done.