That question of “how to judge one volume is good or bad” is decidedly not a childish one! It is also one that does not have a single answer, and different people will tell you different things, no doubt…
In this case, my use of “bad” volume is to suggest looking for “obviously” bad volumes: ones that contain signal distortion so strong as likely not be usable. These include large motion effects, which would exhibit large bright-dark variations in most sagittal images (because of being acquired in interleaved fashion-- slices #0, 2, 4, 6, 8,… etc. and then #1, 3, 5, 7, … etc.). Geometrical distortions due to this might also be apparent. Dropout slices can also be caused by motion, and basically exhibit as nearly blank (axial, for most acquisitions) slices. I don’t really see either such distortion here.
Note that you have pretty large b-values-- up to 3000 s/mm^2. That looks like the data were acquired for HARDI modeling, possibly? You can see that for higher b-values, the data looks less defined and noisier (that is not some issue in your particular data, that is an inherent feature of DWIs acquired with large bvalues). If you just want to do tensor modeling, you might not need all those high bvalues in your tensor reconstruction-- that is something to decide on your/your group’s end, though.
One thing I do note that is a bit odd about those volumes is there is a noticeably and uniformly dimmer band in the superior slices of the FOV. This is most apparent in teh lower b-value volumes at the top. I guess this is a scanner property, and probably not a super desirable one. I emailed one of our local DTI acquisition experts here for suggestions about this-- so hopefully more about this later. It might not be a torpedo for your tensor modeling, as the subject didn’t appear to move much and therefore the relative brightness might be constant for a given voxel across time, and therefore tensor fitting can be done consistently. However, it is probably good to check out.
Re. the “no reference gradient” warning (probably just a warning? can you copy+paste the exact message?) is because the program looks for b=0 as a reference. In your case, you have essentially that with the b=5 s/mm^2 acquisition. I don’t think it should really affect your analysis, but you might see messages about that. Note for future reference, acquiring several reference volumes (b~ 0-5 s/mm^2) is highly recommended. If you only get one and the subject moves during it, your whole acquisition is essentially toast. The reference DWI volumes are really important for tensor modeling so have 4-5 would be a veeery good thing (and even more if you have very long acquisition).