All these are rather elementary examples, and don't require much more than basic critical thinking skills and a little research. There are marginally more informed speculations that make a slightly more careful weighing of the evidence, but even here we need to be careful. For instance, this comment:
Other organisations monitoring extremist groups have noted that Loughner spoke despairingly of a "second American constitution", a reference used by some extreme rightwingers to post-civil war constitutional amendments that ended slavery and gave them citizenship.
Barring actual evidence that this in particular comes from a right-wing source, immediately associating the phrase "second American constitution" with "extreme right wingers" is overinterpretation of the evidence; it's a common phrase, usually deriving from George Fletcher's fairly widely read book on the Reconstruction Amendments. There's no obvious way to tell where Loughner picked it up; conceivably it could be from an extreme group critical of the Reconstruction Amendments or Lincoln-style nationalism, a White Nationalist group, for instance, as some have suggested (largely on the basis of a rumor that has now been disconfirmed), or he could have picked it up from some other source and simply drawn a similar conclusion -- it's not as if it's difficult.
All of this is especially clear given that, as more information has come in, the evidence all seems to point to serious mental illness: the swift descent into wildly erratic behavior over the course of a single year, the apparent disassociation from reality indicated by his repeated references to his being asleep, the compulsion for any sort of order indicated by the very incoherent syllogizing, the obsession with words as constitutive of reality, etc. All very suggestive of schizophrenia or some similar disorder (which wouldn't explain the violence, but would need to be considered when discussing motive). It's very possible that new countervailing evidence will turn up, but at present there's no reason to believe that there is any coherent motive or any straightforward influence in this case.
Whenever dealing with violence of this sort, the only proper response is sober regard for the truth; wild speculation does no one any good and can do much harm.