Disadvantages: rote learning is not as likely to make a long-lasting impression, as opposed to understanding: for example, understanding of the rule for forming Spanish past tense will make you actually be able to use it in the future, and rote learning might mean you will forget it soon.
Advantages: I wouldn't call it an "advantage" but sometimes route learning is simply a necessity: for example when you learn irregular forms of past tense in Spanish.
