4 Bit Register not loading properly
You neglected to say what part number you are using, which makes other people do unnecessary googling. Is it the 40104/40194?

Anyway, it is not true that you send a pulse to S1 and S0.  The values 1 1 should be presented, and take effect on the rising edge of the clock.

If you try to set the inputs to a sequential logic device at exactly the same time as the clock edge, you will get erratic behavior. In general, inputs must already be settled by the time the clock arrives.

For instance, take a look at the timing diagram on page 8 of this datasheet: http://www.datasheetcatalog.org/datasheet/philips/HEF40194BD.pdf

There is a minimum "set up time" and "hold time" before and after the clock edge.