You certainly know that the English alphabet does not contain any umlauts. However, there is a pitfall for German native speakers which often leads to incorrect pronunciation. The difficulty is that in German, the letter y is in many cases pronounced as ü. Some examples are Physik, Rhythmus, System, and typisch. (Listen to the incorrect and correct pronunciations here.) A common mistake is to pronounce the letter y as ü when using words such as hysterical, physics, rhythm, system, and typical in English. In fact, in all these examples, y is pronounced in the same way as the letter i in words such as ring, thing, or king, namely as [i]. In contrast, words which are spelled with an i rather than a y in German, such as crystal (Kristall), are usually pronounced correctly.
Here is a list of words for which the above mistake is often made:
myth, anonymous, analytical, cylinder, cynical, hyper-, Olympia, synchronize, symbol, syphilis, sympathy, synthetic, Syria, synonym
A particularly strange case is logarithm (German: Logarithmus): quite a number of native German speakers incorrectly pronounce the letter i as ü in German and English, possibly because they believe there is a connection with the word rythm (Rythmus).
The pronunciation of y is also an issue when Germans use English expressions in product names and commercials. For example, Garnier have a product line called “Hydra Energy”, but utterly mispronounce “Hydra”:
An interesting problem are German words or names that contain the letter ü, for example, Müsli or Würzburg. In these cases, ü is replaced by another English sound. Therefore, Müsli is pronounced as [ˈmjuːzli] (see here), and Würzburg is pronounced as [‘vɜːtsbɜːg] (see also this post).
While many aspects of the English pronunciation are rather difficult to master, the mistake discussed here is relatively easy to avoid. Just remember: there is no ü sound in the English language.