You bought yourself a good gun. However you might need to clean it. NOT saying that was the issue with the shells, but old Ithacas tend to accumulate crud just like anything that old and as a precision instrument, yes Ithacas are a precision mechanical device tend to work better when clean and properly lubricated.
It is easy to work on an Ithaca if you have a decent set of gun specific screwdrivers so you don't bugger the heads up.
Here is the field maintenance guide
http://stevespages.com/pdf/ithaca_3787.pdf
If you take the buttstock off (remove plate, use a 3/8 socket on an extension (iirc it is 7/16's) to remove the stock bolt, it is a square head bolt with a slot that is hard to remove with a screwdriver) and the spray the action out with some brake cleaner.
The back of an Ithaca action is open, that that is why you take the buttstock off, to not soak it anymore than it already is. They get oil soaked it stored standing up and oiled heavily.
Spray it into all the nooks and crannies. After it dries re-lube the gun.
If you are comfortable working on guns, use the field maintenance guide above as a reference, actually save it / print it off for future use, you never know when online resources will disappear. Take it apart and give it a good cleaning, soak the trigger pack in kerosone, lighter fluid etc.
On the old guns there is a minimum of one spring that needs replaced. The one behind the left hand shell stop. It is very expensive, actually only a couple dollars.
Another overlooked area of the old Ithacas is the magazine tube. Take the mag spring and follower out and clean the inside of the magazine tube with 0000 quad-zero steel wool. once it is clean oil it inside and the spring and put back together. I use a wood dowel with a slit in the end and spin it slowly with a drill. I have cleaned a couple that were junked up and a littly rusty inside
You have bought yourself a fine shotgun that with a little work on your part will be a grand gun.
How is the overall condition ? 16ga Ithacas are my favorite.