According to Yomiuri Online, two men have been arrested for performing "improper acts" in hotel rooms with the same 12 year-old girl on multiple occasions earlier this year. The girl met both men, aged 49 and 36, through her 3DS. Yomiuri Online doesn't specifically mention SwapNote. A Mainichi News report, however, does.
Mainichi reports that charges for child pornography have also been filed against another man, 44, who had allegedly two girls - then aged 11 to 12 - send nude photos through SwapNote, or "Itsu no Ma ni Koukan Nikki" (いつの間に交換日記as it's called in Japan. This man has confessed to the acts.
SwapNote was a free Nintendo-made app that let users create and share hand-written notes and drawings. Users could connect the program to the Internet and, with SpotPass activated, transmit and receive notes. It became available in December 2011. The service ended on October 31.
In the above articles, both Yomiuri and Mainichi note that parents had initially turned off the 3DS's internet function, but the children had turned it back on.
http://kotaku.com/child-predators-were-using-nintendos-swapnote-service-1459304126
The articles in question, both in Japanese:
http://headlines.yahoo.co.jp/hl?a=20131105-00001107-yom-soci [Yomiuri Online]
http://mainichi.jp/area/ibaraki/news/20131106ddlk08040158000c.html [Mainichi]
So Nintendo shut Swapnote because its been compromised.