Plot hole: When Ryan asks Beckett where Castle is, Beckett says something like "I don't know. I thought that the death of a bridesmaid would be right up his alley." and Ryan replies "Probably heard the word "wedding" and got cold feet." Only problem is, how could Castle have known that? He was duct-taped to a chair at the time Beckett called and couldn't answer the phone. We see Beckett right after he falls on the table and we don't see her leaving a voice mail or send a text message so he couldn't have known, especially since he asked "So, bridesmaid huh?"
Plot hole: The security camera images of Castle kissing Kyra on the roof are completely inexplicable. The angle at which the images are taken are near enough identical to the angles at which the rooftop scene were shot. There were no pillars, poles or high walls for a security camera to be attached to at those particular angles, and certainly nowhere a photographer could hide, so where did the images come from?
Plot hole: Brandt sabotages the mercenaries' explosives so they are killed when trying to escape. No real team of professionals would let the rich yahoo who hired them touch their gear. Nor would they use any explosives he provided without (at the bare minimum) inspecting them first. It's a plot hammer to wrap up what happened to the mercs so they can move on to Brandt's capture.
Plot hole: Beckett is framed for the murder of Vulcan Simmons by someone (likely connected to Senator Bracken) who has access to her backup weapon locked in a safe in her apartment. It's never really proven that she's innocent; the murder weapon is never recovered, and the real murderer is never brought to justice. And though she's still technically a murder suspect, Beckett is allowed - after finding the evidence for which she's been searching - to act in her law enforcement capacity and arrest Senator Bracken.
Plot hole: On the recording that Captain Montgomery left for Beckett, the conversation is exclusively between Montgomery and Bracken. But as established in "Knockout", Montgomery was only a rookie during the Bob Armen incident; as two veterans who are more than capable of speaking up for themselves, it seems unlikely that Raglan and McCallister would choose a newbie as their voice, particularly to the assistant D.A who's blackmailing them.