Is there a PDF annotation app for the iPad with minimal (or no!) annoying page transitions?
With a little hunting around, watching videos, and emailing developers, I've come up with the following list.


iAnnotate.  This has good annotation (obviously) and when connected to an external display then the display version has no page transitions (note that there are transitions on the iPad display, though they rate very low on my "irritatometer").  Other pluses: customisable toolbars, and the presentation display doesn't show the toolbars or menus.
There is a slight oddity: even though the presentation display doesn't show the toolbars, the size of the document depends a bit on what toolbars are on display on the iPad.
2screens.  The focus of this is on the presentation, which it does extremely well.  The annotation works in a slightly different way to other apps.  Imagine a glass sheet in front of the presentation and that you are writing on that, not on the presentation itself.  Once you get used to that (so saving and blanking the annotations when shifting slides, I've been told that the developers are working on making this automatic) then it works well.  The presentation part is very nice, with none of the menus displayed on the external dispay.
Explain Everything.  This is, perhaps, a slightly surprising contender as it is really for recording a short presentation (or other).  But it can also be used for the presentation itself and has annotation support.  The external display mirrors the iPad display, but there is a "minimal" toolbar which is very discrete and contains all the main presentation controls.  The only snag with this one is that there is a strange offset with the PDFs that I use (created by xelatex) which means that the slides get successively more out of sync with the backgrounds.  The developers tell me that this depends on the PDF so other methods of PDF-generation may not have this problem (and I'm hopeful that it would be possible to post-process the PDF from xelatex so that it works as well).
GoodNotes (formerly eNote Taker).  This has a little history!  When it was eNote Taker then it worked just fine.  In the upgrade to GoodNotes, sliding page transitions were introduced.  In the current version, tapping on the screen changes pages without the sliding transition so it is usable again.  The display mirrors the iPad display, but the annotation toolbars are very discreet in that they collapse out of the way when not being used.