Modern Hebrew has been filtered through the sound systems of German, Polish, and/or Russian, and lost its characteristically Semitic sounds.
Not quite. Crudely speaking, Hebrew had two separate diasporas - the European diaspora and the North African/Middle Eastern diaspora. Jews who lived on different sides of the Christian/Muslim divide around the Mediterranean basin were isolated from each other by war and the sea, and so two very distinct ways of pronunciation developed. Some of the differences between them have nothing to do with the alphabet, and so I will not go into them here. Just as an example, though, on the Arabic side Hebrew retained all its pharyngal consonants, in keeping with the Arabic.
When Hebrew came to be "ressurected", as Gritchka puts it (although I personally don't see how a language that devolved so much from it ancient origins in 2000 years can be said to have been dead all that time), allowances needed to be made for the pronunciation problems of people (characteristically) from Poland and Morocco. The Poles could never hope to pronounce &ayin or h!êt, but have preserved the gh and dh sounds, which the Moroccans couldn't get their teeth around, as well as having vh (as in war) which I'm not sure was part of the "original" Hebrew. The pharyngal q! and t! were pretty much dead all over by then.
The compromise that was eventually reached basically eliminated everything that anyone couldn't pronounce from the "official" language. Which meant gh, dh, h! and &a had to go. However, one of the things that make Hebrew such a dynamic language is that people who speak it in dialect or a second language are still immigrating to Israel all the time. So even though they might not teach this to linguists, you can still hear plenty of &ains and h!ets all over the place.
At Gritchka's behest, I am appending a note about the whole Sephardi - Ashkenazi Jews thingamypop.
Now. Very roughly speaking, Jews who come from Europe are Ashkenazi Jews (Ashkenaz is actually old Yiddish for Germany), and Jews who come from the Middle East & North Africa are Sephardi Jews. The respective phonologies are therefore known as the Sephardic pronounciation and the Ashkenazi pronounciation.
However. These distinctions are about as historically or genetically accurate a ethnic distinctions generally are, which is why I wouldn't want to make it sound as if these handles are definitive. They're not. They're just handy handles.