Anyone who is not makpid on the ע in keriat shema says apikorsut. He says השם נשבה לאבותינו, which means that He was captured c”v. Similarly, those who pronounce the chaf like the kaf say that Hashem destroys the world out of chesed c”v. On the other hand. those who overcompensate say that געל ישראל instead of גאל ישראל, which is also very bad.
As for the צ, it is clear that at one time it was similar to the “s” sound as the word for stadium in אצטדיון (the א was due to the fact that they could not pronounce a sheva nach at the beginning of a word (Arabs also often do this). Apparently Ashkenazim did not change their pronunciation until later as one of the Baalei Tosafot is
רבי אליעזר ממץ. In French the name of the city is pronounced with a long “s” (you can hear it by going into the Wikipedia article on the city).
Regarding picking up sounds from other languages, it is clear that pronouncing the cholem “oy” or a long “o” (e.g. kosher) comes from Slavic influences. Pronouncing it like an “i” comes from the German ü.