We coupled the laser through a multi-mode fiber into the wavemeter.
With the main amplifier enabled, we got enough power behind the fiber (0.5 - 1.5 mW) to use the wavemeter with 34 ms exposure time (1s / 30Hz to prevent jumps in the wavemeter readout).

Pictures below: 
1: First test scan with 34ms exp. time.
2: Comp. too large laser power (2. scan duoblet) vs. attenuated power (right scan doublet). The latter has less hickups.
3: Laser scan with attenuated power in go4.

The measured frequencies in the first scan step are unstable in any case.

Spikes (rather "second wavelength the laser is regulrarly jumping to") can be removed by adjusting the fiber coupling with the mirrors (change of interference pattern) or the L/2-waveplate (change of coupled power).
However, during (and after) the scan the spikes seem to reappear.