What (if any) are the penalties for putting false information in a planning application? Where would I find any information about this?
I mean for example, in the case of a planning application where the developer has stated that he owns a part of a site which he doesn't and has exaggerated the size of the site holding?

I'm not sure about the penalties, but afaik an application has to be accompanied by a declaration that the applicant has a right to develop the land, either as the legal owner or with the consent of the owner(s) of any other land in question.
Presumably permission can be refused if this is not complied with, or the courts get involved if there is a dispute. Check the legislation on www.irishstatutebook.ie (go to year: 2000, S.I. No. 30, I think, or you can do a keyword search).

Would the better local authority websites not have something? Dublin or Cork City, or Fingal perhaps?