Starting שמונה עשרה late
The gemara in Brachos 21 states that if you come in late you are not allowed to start שמונה עשרה if you cannot finish by kedusha. I find in my experience that many people either don't know this halacha or ignore it.
There is an interesting dispute relating to this halacha. What should you do if somehow you are in the middle of שמונה עשרה and the ש"ץ reaches kedusha. Rashi in Succa says that you should stop saying שמונה עשרה and listen to the ש"ץ and be יוצא שומע כעונה. Tosafos (in Brachos) has 2 questions on this:
1. If this is true then why aren't you allowed to start שמונה עשרה at any time, you aren't losing anything, you are יוצא קדושה through שומע כעונה anyway?
2. If you are יוצא why isn't it a הפסק ?
Tosafos answers 1 by saying that although you may be יוצא with שומע כעונה it is better to say the words (this needs explanation). Tosafos doesn't answer the second question.
We can explain the dispute based on the following. There are 2 ways to look at שומע כעונה:
1. Take the words literally, the halacha is saying that if you listen the halacha views it as if you said the words
2. You are יוצא with his דיבור meaning that you didn't say the words, however the halacha says that you are יוצא by someone else saying the words.
Tosafos would hold like 1, therefore it would be a הפסק because the halacha views it as if you said the words, so you said kedusha during שמונה עשרה. Rashi however holds like 2 and therefore there is no הפסק, you said nothing you are יוצא with his דיבור so it is ok even in the middle of שמונה עשרה.
This relates to Purim as well. There is a minhag to say the עשרת בני המן in 1 breath and for everyone to say them. the Rogatchover explained this by saying that although the whole megilla you are יוצא with שומע כעונה you can't be יוצא this minhag of saying the names in 1 breath. Why not? It would seem that the Rogatchover holds like Tosafos, and therefore שומע כעונה makes it like you said the words but it can't add anything over and above that, so you said the words but not in 1 breath. However, according to rashi you are יוצא with his דיבור and his דיבור was good (in 1 breath) so just like he is יוצא with his דיבור you are as well.
The same question comes up as well by bircas cohanim. Can 1 kohen make the bracha and all the other cohanim will be יוצא with שומע כעונה? The Beis Halevi said no because bircas cohanim requires קול רם that everyone in the shul needs to hear you. It would seem that the explanation is the same as for the עשרת בני המן that שומע כעונה can't create קול רם.
One final point, we pasken like rashi that a person should stop and listen. There is a machlokes acharonim how should the ש"ץ say kedusha, should he say the verses קדוש קדוש and ברוך כבוד with everyone or after everyone. The Mishna Berura says with everyone because otherwise when he repeats it it is not called בציבור, others say that if he says it with everyone then we miss out on this din of Rashi (because they can't hear the ש"ץ and be יוצא through him as he is drowned out by everyone else and no one else has כונה to be מוציא), therefore they say the ש"ץ should specifically wait until everyone is finished to fulfill this din and they say that it is called בציבור because he is the ש"ץ and saying it in that capacity.
Anyone who davens for the amud should really ask their Rav what to do when saying kedusha, like the Mishna Berura (with everyone) or afterwords (or a compromise to be יוצא both).