Depending on the lens and model of Nikon, you will probably not have autofocus or auto exposure controls, etc. Nikon has information on their website about what lenses can be used with what models. Also, newer lenses have optics that take advantage of newer glass and computerized design systems and are designed specifically for digital cameras. Of course there are older classic lenses that have great optics that will perform optically just great, but you may be doing manual focus and exposures.
I have a Nikon SLR, and I plan to buy a Nikon DSLR, but I have some budget restrictions. Which would be the cons of using the old lens on the DSLR for a while?