1) The Flying Spaghetti Monster reductio
The Flying Spaghetti Monster historically arose as a reductio ad absurdum argument against teaching ID in schools. If ID can be taught in schools, the argument goes, then the equally scientific notion that a Flying Spaghetti Monster created the world must also be taught.
It should be obvious that this does not reduce ID to an absurdity at all. If anything it is aimed more at young-earth-creationism than at ID. ID is agnostic about the identity of the designer - all it claims is that the designer was "intelligent". So insisting that a particular theory about who the designer might have been is clearly outside the bounds of what ID is proposing.
2) Who Designed the Designer?
Another common argument against design is "Who designed the designer"? Since the designer that ID posits must have been really smart and really powerful, he was presumably also very complex. But if he was complex then he requires a designer, which results in an infinite regress.
Many things could be said about this. Interestingly enough, according to the Christian doctrine of divine simplicity God is not "complex", and thus wouldn't necessarily warrant a design inference. But completely aside from that, ID is an empirical science, and as such is only interested in drawing inferences based on observable data. No design theorist would suggest that it is valid to infer design for something that had not been observed.