I simply had a pig on a lead and used my mouse wheel to select a fishing rod. I right clicked as normal to use the fishing rod and the rod worked as normal. When I right clicked to bring the fishing wire in, another fishing wire was created, again and again (see pic).
Step by step
1. Place a fishing rod and a lead on your hotbar
2. Right click on an animal (in my case a pig) to attach it to the lead
3. Use your mousewheel to scroll to your fishing rod
4. Right click with the fishing rod mutliple times
5. You'll see multiple fishing wires
can't reproduce, tried it with a sheep and a pig on multiplayer survival and singleplayer creative, while looking at a sheep and while not. catching a mob with a rod doesn't work either. Windows 7 64