The most obvious ones would be the names of those two religions themselves, Muslim/Moslem and Hindu/Hindoo, though I could probably rattle off a couple dozen of them ranging from proper names (sects, religious figures, local ethnic groups, placenames, etc.) to cultural practices, foods, crafts, and god knows what else if you gave me an hour to think about it. So long as the right phonemes are being expressed and everyone knows what word it is when they see it, I don't really understand how one anglicized spelling can be considered "more accurate" a translation than any other when the language of origin uses an alphabet that doesn't precisely correspond to the Latin alphabet anyhow (not that the Latin alphabet precisely corresponds to itself half the time either, but that's beside the point).
The point of transliteration is not merely to approximate the original sound, but to be a single consistent system. Older names were adopted before consistent transliteration schemes were created. People would just write their best guess as it sounded to them, and so they weren't consistent with standards adopted later. There are more aims too; another good feature is to allow someone who does know the original script to be able to understand what the original untranscribed word was.
For instance, tone marks in Pinyin are of no use to someone who doesn't speak a tonal language, much less know the Chinese ones, but they're critical to someone who does know Chinese to understand which word is meant (unless context makes it obvious; clearly they know where 'Beijing' is even without tone marks) Another example is "shch", which is the standard transliteration of Russian щ. It appears to be two consonants; "sh" and "ch" but the letter щ only represents one. The non-obvious logic here is that it's roughly a "sh" sound pronounced with the tongue in a "ch" position, and the the point is to distinguish it from the "sh" which is ш. Both of these are liable to be pronounced simply as "sh" by an English speaker regardless, but distinguishing the letters was considered important here. Consistency often takes precedence over accurate approximations; Russian 'о' ois always 'o', 'и' is always 'i' even though vowel qualities change a great deal in Russian depending on where they are in a word and if they're stressed. e.g. 'Борис' becomes 'Boris' and gets pronounced as 'BORE-iss' even though it's really more like 'buh-REES'. Since English simply does not have Russian vowel reduction, either one must be consistent with the transliteration and accept mispronunciation, or give every word its own transliteration, which would be a mess.
Besides the inconsistencies caused by not having transliteration standards, there are also inconsistencies that stem from the transliterations being of names/words in third languages or dialects. For instance, "Peking" was not actually a transliteration of Mandarin "Běijīng", but the Cantonese pronunciation of it; "Bak^(1)ging^(1)".
Anyway, so the story of words like 'muslim' is that a spelling was adopted that conformed better to the "standard" transliteration of Arabic. In-itself it is not necessarily better or worse. But having a single consistent system of transliteration is far better than trying to maintain a historic hodge-podge of different approximations. (although to an extent we do, where names/words are just too ingrained to change, e.g. Moscow is not likely going to change to Moskva in English soon)