Homophones are words that have the same sounds but different meanings, or at least that is the definition I will use here, I am sure that there are some linguistic wrinkles that add complication but I will ignore those. Homophones can be a big headache for language learners and the occasional cause of mistakes even for native speakers, basically speaking it is unlikely that any rich language will possess enough sounds to make every word sound distinct even if multiple syllables are used. It could probably be done by design, but languages evolve over time. Many languages have enough redundancy that homophones are not likely to clash (the context makes it clear which word is being used). In some languages (Mandarin Chinese for example) the number of sounds and the structure of the language (each syllable having a meaning) have resulted in the tone of a sound contributing to the meaning (so sounds that would technically be homophones in English aren't homophones in Chinese unless the tone is the same).
Thai is a tonal language and to some extent presents similar problems to Mandarin Chinese, but in my opinion Thai is somewhat easier for a learner in the area of homophones. I will start with the difficulties of Mandarin and then show why I am finding the sounds in Thai somewhat easier.
Not enough sounds
Mandarin Chinese has a limited number of sounds compared to English, tones are used to pack more information into each sound but even then native speakers still typically need more context to select the meaning of a word (in English even a random, seldom used word in isolation can often be understood if spoken clearly). For a learner just starting out, you can't distinguish the tones without practice so now you have so many homophones it seems impossible to select from the possible words you hear. To put things in context a learner of English may get frustrated with "to", "two" and "too" but to be fair there aren't many common homophones in English that can be confused in the early stages. In Chinese if you can't catch the tone then the words for "buy" and "sell" the words for "there" and "where" etc. are homophones (a bit of a headache).
Poor loan words
Many languages have English loans words, Chinese has a fair few, which is great, the problem is that because Chinese uses characters from its writing system to represent them the sounds are only close approximations to the English sounds and are not easy to remember at first. For example "party" becomes pai dui. This potential source of easy words is not so easy after all.
Single syllable meanings
Essentially in Chinese every syllable has a meaning and is represented by a single character with meaning in the written language. Written language can be quite compact and is especially so in classical Chinese. The characters (of which there are thousands) map well to meanings. In spoken language often words are constructed by ramming together two syllables of similar meaning to make the word distinct enough when spoken. This effect becomes even more noticeable when you start listening to Cantonese as a comparison. In Mandarin bu zhidao means "don't know". In writing (and sometimes speech) just the zhi part can often be used for "know". Cantonese has a fair few more sounds than Mandarin and you are more likely to hear m ji rather than m jidou for "don't know" (there is more redundancy in the sounds so a little less need to create two syllable words for spoken meaning).
Initially Chinese can sound just like a stream of syllables of which you have to pay attention to every single one just in case.
Where Thai is a little easier
Thai appears to have more sounds than Mandarin, reducing the number of those troublesome homophones, even accounting for the tones.
The English loan words in Thai are basically pronounced the same as in English but with a heavy Thai accent (naturally) this means that once you get used to how Thai people speak English then the loan words are easy to remember and pronounce. They also are very unlikely to collide with existing Thai words so won't from more homophones.
Alongside the loan words from English Thai has picked up a decent number of Asian loan words, injecting a generous amount of multi-syllable words that can be distinguished.
Thai of course has it's own hardships and some aspects are harder than Mandarin (saving those for later posts).
Listening is important
Listening to the language you are learning and taking time occasionally to pay attention pays huge dividends. I haven't read about homophones or these elements of the languages I have been paying attention to (although I did read somewhere about Cantonese having more sounds than Mandarin and a few other things). It is quite possible I am actually wrong about some things (Thai having more sounds than Mandarin for example), but the things I notice help me learn. I can start guessing that there are no Thai words that sound like English "hay" or "may" and no Thai word that sounds like howzhai (rather than kaozhai) because these sounds are freely substituted for the sounds of other Thai words (which mostly wouldn't be allowed to happen if it caused homophone issues).