None...
Movie 1 and 2 would probably hurt the overall manga canon the least, and Gosho did integrate Shiratori into the manga canon from M1 (so that would probably be the best choice). However, almost every movie makes Conan/Shinichi too perfect (the running gag of "I learned it in Hawaii"). I can believe Shinichi knowing how to fire a gun, but not with the level of accuracy in M2. M3 would have had Conan die due to the bullet proof glass glasses (impossible) and Kid finding out his identity. Same with M4 and boating, with the inclusion of the possibility of another kink in Shinichi's story due to that ShinRan scene towards the end. She can be dumb, but surely she would have realized that Conan was out of earshot of her mother's story and thus that scene wouldn't have worked. M5, though my favorite movie plays the BO is a less than ideal manner for the manga canon. Gin is not so careless as to take aim unless he is 100% certain of his target and was sure he could make it a perfect crime, and shooting Sonoko would be bad... Killing the daughter of a major corporation does not work. M6 was just... so very unlike DC... Having that included would be horrid to manga canon. M7 adds to the HeiKazu story that doesn't entirely work, and same with ShinRan for that matter. In terms of abilities Shinichi was downplayed in lieu of Heiji, so that isn't an issue so much as the relationships. M8 is worse than M3 for Kid, cementing the fact that Kid knows Conan's identity, and it also puts him OOC, because not only would he NOT disguise as someone whom he couldn't mimic 100%, but he wouldn't put himself next to someone who could see through it in an instant (same issue with M14 in terms of Ran/Shinichi/Kid interaction). M9 has its issues with the Kogorou/Eri story. It would be nice having Kogorou successful, but not at the cost of the destruction to manga. There is probably more but I can barely remember any specifics. M10, no...just... no. Don't know why it is popular, but it doesn't work on multiple levels, including the scheme to make all of those detectives in on the overall scheme. M11... another... just...no. That was the anime teams idea of writing Conan as Indiana Jones, with Ran and Sonoko being pirates for...some...reason... M12 is another where parts would work, but overall it messes with character ability and tries to make them too perfect. Conan is confirmed to have perfect pitch, but he cannot hold a note. So that movie doesn't work there. I'm sure there is more again, but haven't seen the movie in a while to determine with any certainty. M13... sure Irish is awesome, he would make a great BO member, but he seems too much like Bourbon at this point (ironic that they are both whiskeys). It also had severe issues with BO being OOC. Destroying major property in a big way that would illicit military intervention? Ha that is a good one. M14 is just horrible on several levels. I don't want to get into it. M15 has more inclusion of things that wouldn't fully work within manga canon including Shinichi's abilities, and some inherent physics conundrums that the movies have been so very known for.