Spanish is a language in which it is not necessary to specifically name the subject of a sentence with a pronoun or otherwise. If I say canto, it is obvious that I am doing the singing because the verb cantar has the unique o ending for the first person singular. However, when we are dealing with the third person singular, (canta), we really don't know who is doing the singing without a context. He/she/it/the wind?/ sings. It gets even worse in the imperfect. Cantaba can mean I sang/used to sing, you (formal) sang/used to sing or he/she/it/a frog sang/used to sing.
Then we have su/sus. This word could correspond to his/her/its/your (formal singular and plural)/their. If there are several persons involved in an account and the text is not clear enough, it can be a potential pitfall to the translator.
Fortunately, most of the time, legal texts are fairly straightforward -barring the famous legalese, but that is a different problem. Legal language provides lingustic safeguards such as "del mismo/de la misma/de los mismos/de las mismas" to signify his/her/its/their. Similarly, if there is more than one person involved in a suit (there usually is), then you will commonly see "el primero/la primera" and "el segundo/la segunda" to signify the former and the latter.
In my experience, I have found that the ambiguous language comes from transcribed oral proceedings such as a reply to interrogatories (prueba confesional) where the respondent is required to answer questions about the facts of the case and his/her answers are written down. There is often a context which the translator is not entirely privy to, and the information is not presented in legal language.
My answer to this potential ambiguity is to read the unclear passage of the source text several times and, at the same time, ask myself "Who is doing what to whom?" There are usually several clues to help sort out the details.