I'm having trouble interpreting this southern blot.

Yes, that seems quite strange.
I'd expect that the glu1 gene was cut in various random sites from mnase. Note that, it specifies that the digestion is "limited" meaning there should be lots of different random pieces. So, each band could represent a separate piece of this gene.

So, what is the meaning of this southern blotting? Maybe it is used to determine whether the gene is active or not. Remember that a mnase cuts more often the single stranded DNA. Since the strands of an active gene are separated, the mnase will cut more often the active gene, and will produce more bands.
In our case, the gene should be active at the yeast grown in galactose. So, in the corresponding southern blotting, we should expect more bands.
To be honest I don't see notable difference between the two southern blotting. However, with some imagination, you could distinguish a couple of extra bands found only at galactose-grown cells.

I'm not sure if that helped... I don't even know if it makes any sense. I hope someone with more knowledge will help us figure it out.

I think the difference we are suppose to be noticing between the two blots is at the UAS site. In gal the bands(which i presume to be chromatin) are shifted upwards. Maybe this is telling us when Gal is present, chromatin remodeling is occuring to allow for the Gal1 gene to be activated

I think now I understood more about the certain mechanism. Mnase cleavages the DNA out of the nucleosomes. As I said earlier, each band represents a part of the gene. But, if you see carefully, you will notice that the distance between the bands (in bps) is constant. I think this means that, the first band represents the DNA located in one nucleosome, the 2nd band is the total DNA in 2 nucleosomes etc. That is possible, because the digest is limited, so there should be some cases where the DNA between two nucleosomes was not cleaved.

That makes perfect sense, but now we must explain the hard part... Why are the blots different?
The main difference between the two blots is located somewhere between the 3rd and the 4th band. There is a dark spot there (an extra band?).

We could hastily conclude that, when the gene is active, some changes at the UAS promoter is causing the certain region of DNA to remodel, possibly driving away the certain nucleosome and allowing the mnase to cleave the certain site. (see attachment. The circle DNA part represents the new band on the gal plot)
But the problem is that the mnase would be able to produce many more combinations of DNA, which would produce much more bands....

Concluding, I can't find any specific mechanism that could explain these results... sorry . I either didn't fully understand the mechanism of mnase or the exercise has some faults...
I also don't know if I was understandable, so ask if you want.