As a native Spanish speaker I can say...
- Unnecessary bureaucracy: until a word is accepted by the RAE (Royal Spanish Academy) the word does not belong to the language. And even then, you sometimes end up with monsters like "cederrón" (for CD-ROM).
- OMG, irregular verbs: there are a lot of irregular verbs. The amount could be lower than in English, but in English you have to learn 3 forms of the verb, at most, whereas in Spanish you could easily have 20 irregular form for a single verb.
- Spelling is unnecessarily complex: due to historical reasons, a lot of letters exist that are not necessary anymore. H is always silent (except in CH clusters), C can be replaced with S or K (depending on the vowel following), Q is unnecessary as well.
- Sexist. You don't have neuter words for a lot concepts. For instance, "Spokesperson" and "Spokesman" is "Vocero". You can't infer just by the word if it is a man or if the speaker doesn't want to specify the sex of the person.
- Lots of tenses: who the hell uses the "pasado anterior" (e.g.: hubo ido)? It doesn't make any sense to have such a tense, only used by people who want to show off their skillz of the language (probably literary cunts).
Hope you can win the discussion ;)