Nadav Shragai says in Haaretz that Jerusalem District archaeologist Gon Zeligman, does not believe the renovations of the "Solomon Stables" are connected to the current problem, but thinks it is the result of faulty construction. The wall is part of shoddy building additions from the 19th century. In this respect his view differs from that of Dr. Eilat Mazar from the Committee for the Prevention of the Destruction of Antiquities. Another possibility cited in Haaretz' printed edition but not in the online translation, suggests that the Waqf works changed the way the (rain?) water trickles into the mountain, causing the bulge.
This photo clearly shows the bulge:
Here is another really good photo and a sketch explaining exactly where the bulge is. Unfortunately the explanations are in Hebrew but it will help you get the picture. The bulge is on the lower right side, denoted by a little black frame with white writing and an arrow pointing at the wall. The nearby mosque with the silver dome is Al-Aqsa (The Golden Dome of the Rock, is not Al-Aqsa, contrary to popular Western belief, but a marking of the place where Muslims believe the prophet Muhammed landed when he flew to Jerusalem on his winged horse, one night). The Western Wall is on the lower left side.
Yet another Update: Tal G. has something better - a very clear aerial photo and a translation from Yediot Aharonot, which gives some different information about when the wall was built than Haaretz. Nice to see everyone agreeing about the facts.