Wine making - problem solving

I am finally moving forward in the wine making adventure.  I ran into a bit of a snag on the whole process right at the beginning and wasn't sure what was going on.
I had everything mixed together and sealed in the bucket.  I was checking in on it daily like the directions stated.  The goal is to give the mixture a stir and to measure the specific gravity as the wine ferments.  After a couple of days, I got worried.  The specific gravity wasn't changing.  In fact, nothing seemed to be happening at all.  I added some yeast nutrients to see if that would help.  It didn't.  The only other thing I could think of was that the yeast that had come with the kit had gone bad.  I had no idea how long that kit sat on the shelf before I bought it (or if it was exposed to extreme temperatures).  It took me a week or so to get over to the local wine making supply store, but I finally purchased some new yeast.
The new packet of yeast did the trick!  The day after I added it, I went to check on the "must", and was surprised at the change I found.  The juice was bubbly and acted like champagne when I tried to measure the specific gravity (lots of fizz and bubbles).  It continues to progress and tonight the specific gravity is getting closer to where I need it.  Today it smells like alcohol.  It is encouraging to see the change after the frustration of a couple weeks of nothing happening.
My only concern now is that I added too much yeast nutrient to the must.  I don't know what that will do to the finished product -- if anything at all.  Only time will tell.
Soon, I should be able to move the wine to the secondary bottle.  I'll have more photos at that time.