Besides coherence length, another important property of a laser is its stability against mode hops. A mode hop (or jump) refers to a sudden change of the longitudinal mode spectrum, which typically occurs when the currently lasing mode drops out of the laser medium gain profile (eg, due to thermal expansion of the laser cavity), so that suddenly another mode at a slightly different wavelength has higher gain and so will start to lase.
Its effect on a hologram is a reduced coherence length, in some respect quite similar as if several longitudinal modes lase simultaneously. Indeed, whether several different longitudinal modes are present simultaneously or whether they just lase one after the other, doesn't matter much: in each case interference fringes are blurred, and the severity of this effect depends on the frequency (or wavelength) difference of the involved modes (for mode hops the blurring also depends on the fraction of the exposure time during which a given mode lases; obviously a very brief hop to another mode will not matter much. In the following, we will assume for simplicity that all involved modes contribute during the same amount of time). Therefore, mode hops are much more serious for lasers with a large mode spacing or short cavities, such as diode lasers. For the latter, the mode spacing is like 100Ghz, so one single mode hop during exposure time will effectively cut down the coherence length to a few mm or less -- pretty much ruining any hologram by giving it a "sliced bread" appearance. On the other hand, for a single mode argon laser, a mode hop effectively reduces the coherence length to roughly the length of the resonator, which does not matter for most holographic applications.
Therefore, preventing mode hops is crucial for diode and other lasers with short cavities; the most common and important method is to stabilize the temperature of the laser to a fraction of a degree.
The situation turns out to be even more delicate for extended cavity ("ECDL") designs, where an external grating is used to extend the cavity length from a mm to a few centimeters; while such constructions can do very well for atomic spectroscopy, they appear not to be too useful for holography due to stringent requirements for temperature stabilization, and a delicate setup requiring spectrum analyzing tools; see the investigations here.
Related issues are smooth mode drift (without hops) on one extreme side, and chaotic mode competition on the other. If the temperature of a laser diode is slowly changed by a small amount, the cavity length smoothly changes and so does the wavelength of a given longitudinal mode. Even if no hop to another one occurs, the mere wavelength shift can also effectively reduce the coherence length and therefore must be small enough (as a rough estimate, the temperature of a laser diode must be held constant to a hundredth or even to a thousandth of a degree Celsius, during exposure time. For a more detailed discussion, see here). Now, if we go on and change the temperature even further, a discrete mode hop may occur where the wavelength suddenly jumps by a larger amount; this is what we have described above. However, much worse than this can happen: in the transition zone, two (or even more) longitudinal modes can compete in such a way as to yield a chaotically fluctuating spectrum. If a diode runs in such a regime, it is totally unsuitable for any holography use! Whether hops are simple or chaotic is hard to predict, and depends on the precise operating conditions of the laser diode. For an illuminating review, see here.
Detecting mode hops:
Simplest is to look for AC noise in the output of a photodiode via an oscilloscope, or just listen to it by coupling the photodiode to an audio amplifier. This is quite instructive and gives some idea about the behavior of your favorite diode laser. Below is a picture of the AC output of a photodiode that shows first a transition through a chaotic regime, and subsequent simple mode hops (1sec/div horizontal scale, picture taken from here):