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The shows blatantly violate the phonetic constraints of the language. For example, "Worf" is not a valid Klingon syllable because there's no f sound or letter in Klingon.
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Pronunciation within the shows is massively inconsistent. For example, people say "gagh" like /gak/, /gaɣ/, /gax/, /gakx/, /gaχ/, /gaqχ/, /gakʼ/, /gaʁ/, and /gaħ/.
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The phonological inventory, which is supposed to be "alien", is pretty clearly inspired by indigenous languages of the North American Pacific Northwest, and is honestly less strange than some real human languages like Ubykh or !Xóõ.
- oh and the Latin spelling is terrible!
it's case-sensitive and each letter is required to be either upper or lower case, but seemingly at random. the only time the two cases of a single letter actually represent two different sounds are q and Q.
Q represents the uvular affricate /qχ/, which you could definitely write more elegantly as qx, x, or qh.
I have to assume the mandatory case for letters was actually just an attempt to make it look more alien and not done for any reason related to making the orthography practical or realistic or elegant.