I read somewhere that cognitive tests like the Weschler are not always useful for parents when an appeal is lodged. Does this mean that sometimes people are disappointed with the scores
The Weschler tests are very reputable, but it's obviously a possibility that your child may not get the scores you were hoping for.
or that the panel do not take these reports seriously?
Panels do have a duty to consider any relevant evidence properly - but it's up to the individual panel just how much weight they give to any particular piece of evidence.
What sort of score might impress the judges- would 130+ be required?
This will depend on local circumstances. If it's a superselective school where entry is fiercely competitive, for example, it would probably be advantageous to have results towards the very top of the range.
Also, clearly, lots of us think that our children should have a place at grammar school but what sort of grounds would win an appeal? Would they be, perhaps, something along the lines of your child being so strong in a particular area that they are unlikely to find peers of a similar ability in another school (backed up with evidence to show that this is likely to be the case)?
There are one or two comments in the Q&As about what might or might not be a strong argument.http://www.elevenplusexams.co.uk/appeal ... -school#c2
However, it's impossible to be very specific about this, because it depends on other factors (e.g. how strong a case the admission authority puts forward to resist further admissions, perhaps how strong other appellants' cases appear in relation to yours).