Several basic things can be done to prevent modehopping in DPSS laser systems.
Generally, DPSS systems will use an Intra-Cavity aperture. This forces the laser to only run in a single mode. This can either be a physical pinhole, or a pump aperture. A Pump aperture is done by pumping a small cone in the lasing medium to prevent other modes from getting gain. These can also be used together to further force single transverse mode.
If you have a cavity without any aperture, it can lase single mode with the correct mirror configuration. On most small DPSS lasers, one or both of the mirrors are coated onto the crystals. This presents a problem for two reasons:
First, the mirrors are both flat meaning you have an unstable resonator, allowing any mode to lase.
Secondly, you get an effect that is called thermal lensing. This happens because the active area of the crystals expands due to the heat. The result is that you will get different cavity shapes, some of which only support non-TEM00 modes.
The combination of these in small crystals with unregulated temperatures can cause severe mode hopping problems.