In the article titled "Winterizing Your Boat" by John E. Brady, I came across the following line talking about draining the lower unit oil:

Also check for metal filings, milky appearance, or black color with burnt odor. If old lube has any of those characteristics, see your dealer.

Last fall when I changed the LU oil in my boat, it was very dark in color and smelled like it was burnt. I asked around some guys I know who have boats, but nobody was quite sure what that meant, and that I should just keep an eye on it. I planned to change the LU oil again earlier this season, but I didn't use the boat as much as I had planned this year, so I haven't done that yet.

Does anyone know what the black color with burnt odor means? Am I looking at a serious problem with the lower unit?

I think that means the seals are leaking in the lower unit and its letting exhaust gas in the oil which is heating it up and burning it. Burnt oil doesn't lub good. I would get the seals changed

black or burnt smell usually means low oilor has just been used alot since last oil change