For reference, if my counting is correct, Mandarin Chinese has:

  ~1465 syllables considering tone (is there a word for this?):
    ~416 syllables ignoring tone:
      21+1 initials (b, p, m, f, d, t, n, l, g, k, h, j, q, x, zh, ch, sh, r, z, c, s, empty)
      35+1 finals, consisting of a subset of the possible pairs of:
        3+1 medials (empty, i/yi, u/wu, ü/yu; but note that "u" is used instead of "ü" after some initials)
        10+3 rimes (empty, e, ê, a, ei, ai, ou, ao, en, an, eng, ang, er; note however that the spelling often varies based on what initial and medial precede it, in particular this is how "o" appears in several unrelated places):
          ?6+2 combined non-medial vowels (empty, e, ê, a, ei, ai, ou, ao; but this isn't a particularly meaningful thing to count since medials can occur without a main vowel, and there are so many irregularities of the pronunciation and spelling)
          2+2 codas (empty, n, ng, r; note that "m" can also appear as a syllable of its own but is an initial with a vowel that has been lost, unlike "r" which is clearly a bare coda with a practically-absent vowel; syllabic "n" and "ng" are bare codas unless for a character also pronounced bare "m")
    4+1 tones (¯, ´, ˇ, `, and neutral; neutral tone is only allowed for a handful of syllables; fairly often only 2 or 3 tones actually exist for a given syllable)

Most of the weirdest cases are for interjections and core function words - only a few characters, but fairly common in (informal) speech. But note that Pinyin absolutely is a mess of exceptions, not any kind of organized thing, and only some of that can be blamed on the fact that it's trying to model human speech.