One major annoyance that I had with the plot was the abundance of "deux ex machina" moments. These are moments in a story where the characters seem to be in a hopeless situation, but then something completely unexpected or unrealistic comes along to bail them out of it. This kind of plot device is okay if used in moderation, but it happens way too many times in Da Vinci. To wit:
(Spoilers ahead... although the spoilers basically amount to: they don't die.)
- Robert and Sophie are trapped in an armoured truck. A villain is pointing a gun at them. Instead of just shooting them, the villain decides to close the door of the truck, right onto a bullet shell casing that Robert had just happened to kick into the doorway. The door bounces back and the villain comically bangs his head on it. Yes, yes, I know in the book some explanation is given as to why he pushed the shell casing into the doorway... but really, I'm not going to go and read it again.
- Robert and Sophie are standing in some church. A villain is pointing a gun at them. Suddenly, a dove flies by and distracts the villain, who then proceeds to forget how to shoot a gun. He fires and misses. A dove flies by! What is this, a John Woo movie?
- Ian McKellan is sitting in his house. A villain (Silas the crazy monk) is pointing a gun at him. He grabs his crutches and swings. Incredibly, Silas, who we have just seen killing a nun with a single, well-timed and ruthless strike, fails to react fast enough to shoot Ian McKellan at point blank range. I would expect Jackie Chan to be able to pull a move like that off, but Ian McKellan? And this isn't Gandalf Ian McKellan. Or Magneto Ian McKellan. It's crippled scholar Ian McKellan!
And that's all I have to say about that.