Hartshorne and Ullman (2006), testing hypotheses about how males and females learned language, expected to find that girls "regularized" irregular verbs (like "holded" instead of "held") less often than boys. They found just the opposite; girls used "holded" more often than boys. Ullman's theory about declarative vs. procedural language learning (see his
2001 review for detail and competing views) does not seem to be confirmed by the 2006 experiment, but the words that girls tended to "regularize" were words with rhyming regular verbs (as in "holded" rhymes with "folded"). This was not true for the boys in the experiment.
Hulle et al (2004) tested vocabulary and two-word pairs in pairs of twin toddlers to determine how much of their language use was environment, genetic, or gender-based. While the greatest effect was shared environment, heritability seemed to be a bigger factor for boys than girls in vocabulary -- and higher for girls than boys in two-word combinations.
Interestingly,
Catalan's (2003) study of Spanish-speaking adults learning a second language found that women tended to use rule-based strategies more often, while males tended to use vocabulary lists.
Ullman's 2006 study used a sample of 25 children, with ages between 3 and 5 years old (the boys were slightly older, but not in a statistically significant way). One factor that I didn't see addressed was the subject of cuteness. In my experience, children are well aware of the effect that "cute" errors can have on adults, girls are more prone to purposeful errors than boys, and breaking them of "cute" habits is really hard. Of course, I'm having a really hard time remembering the developmental difference between 2 and 5, which is huge. It could be that these studies are correct in their assumption that the children don't know any better, and that "cute incompetence" doesn't emerge until later. A lot of my experience with improper word use comes from adults; I've broughten my own baggage to this subject.