Improper weld current selection can cause problems during resistance welding. The problems normally show up in the form of expulsion, indentation, electrode sticking, mushrooming or low weld strength. There is an ideal current range for every resistance weld set up. This will produce good weld nuggets with little or no expulsion, modest indentation and minimal electrode wear or sticking. Whenever you push the extremes of the current in the weld window either high or low you risk problems.
High currents insure that you will get the part hot but probably hotter than is required. This may in turn create excessive electrode indentation. It can lead to metal expulsion since there is a large amount of energy and molten metal present.
This excessive heat can also cause the surface of the work piece to be hotter which can lead to sticking of the electrode to the work piece. This excess heat on the surface will also cause the electrode to wear faster which will show up as premature mushrooming. Finally expulsion can occur at the surface, which can damage the electrode face. Expulsion is always bad since it is a safety issue.
Low currents of course can lead to small weld nuggets and low weld strength or no weld at all.
References: RWMA - Resistance Welding Manual 4th Edition