I think the experiment that was refered to above went as follows:
The participents were asked to assess their ability to correctly guess the outcome of a random number, as to whether it would be higher or lower than the previous one. As the numbers were random there was, of course a 50% probability of being right. Non depressives were more likely to rate their chances higher, and also to rate the chances of others in the same situation as higher. Depressives were generally more realistic about the chances of others, but were significantly lower in their assessment of their own ability, giving themselves a far lower chance of being correct.
One factor that has not been mentioned in regard to depression and weird stuff is schizotypy. This a measure of the weighting that individuals give their own thoughts over outside factors. When people get a high score on a schizotypy questionaire they are often worried that this makes the more likely to suffer schizophrenia. This not the case, but schizophrenia is an extreme example of schizotypy, where the individuals interior world comes to outweigh evidence of the outside, objective world. Depression, it seems to me, makes the individual more prone to schizotypy, as depression alters the functioning of the body slowing it down, making it less efficient. When suffering from the symptoms of depression, sensory input is not as vivid, because the processing of that input is hampered by a general slowing down of the person.
In this gap, subjective 'thought based' perception is interpreted as stronger, that is 'more real' than in a person who does not suffer depressive symptoms. This it seems to me would make a person more prone to perceptual 'mistakes' and to being more certain of the 'reality' of those mistakes, with the thought based understanding of an experience becoming more important and stronger than the objective truth of it.
'Wierdness' lies at that exact boundary between an actual concrete occurence and the sense that the mind makes of it.