Hi Neil,
Happy New Year!
The Social Security Death Index is just what it says it is...an index. It will have his birthday and depending on when his death was filed it may just have month and year. Later records will have exact (if known) death dates. Also beware the death location may be different from the last residence.
If you go to this website:
http://www.ssa.gov/online/SSA-711pdf. It will tell you how to order an original copy of his social security application. If you "Google Social Security Administration" you will find that the rules for getting access to his file have changed and it doesn't seem to be worth the money any longer.
If you are looking for the name of his spouse, do you have his marriage record?
Hope this helps,
Laurie