Lots of potential issues with this chemistry.
1) How old is the acetic anhydride? Was it sealed well? If it's old and people haven't been careful with it (ie; left it open on the bench for a long time) then a lot of it could be hydrolyzed. Also, how many equivalents are you adding? For acetylations, I generally added 3 per group I was trying to acetylate, unless the bottle was brand spanking new.
2) There are more things besides the hydroxyls that can and will react with an acylating agent. The phosphate for one (though they are weak nucleophiles, in the right conditions they can act like a carboxylate and be much more reactive) as well as the aniline (also not a great nucleophile, but good enough to be a problem). The mass spec might tell you how many things have acylated, but knowing where they've acylated will take some detective work, and it won't necessarily be straight forward.
3) DMAP needs to be washed out under acidic conditions, neutral will not be enough.
One of the more common ways to protect the hydroxyl groups of nucleosides is to make the acetonide. I would explore that rather than acylation, this seems like more of a headache than it's worth.