First is probe bending. Probe tips vary in stiffness depending on the material, it is always better to keep probe tip as short as possible, typically lighter weight probe tips are not as stiff as heavier probe tips
Example going from a from a 60mm stylus to a 250mm probe tips on a CMM with an accuracy of .5 + L/1000 has shown a change in measurement accuracy of 2 micron, while this is small it could have an effect on tight tolerances measurements that require longer probe tips
Second longer probe tips magnify machine errors, errors such a straightness, pitch, twist or yaw, can be significantly magnified by the probe length.
An example would be the manufacturer states that a 60mm probe is used for proving machine calibration results. If you have a feature that requires the use of a 240 mm long probe tip, you could see the amplification of the error of the machine error 4 times greater than the results shown in the machine calibration
If you are looking into purchasing a CMM it is recommended that you define your tightest tolerance measurement and insure that the machine has the accuracy capable of performing to this requirement, if that measurement requires a longer stylus you may want to have a demo on the part to see the results, it is even better if you right a performance specification into your purchase spec for the CMM