I have used my Rode on camera to video fairly strong sounds (waterfalls, trains, aircraft...) and the quality is better than the built in mic, just! The biggest difference is to get your mic as close as possible to the source, as the other guys have also said, either using your Rode on a boom with an extension lead, a lavalier or using a digital recorder. Some of these start at around £$70 so are not too expensive and give you full control and much better sound, either using their built in mics or your Rode as an input. I have used my video mic pro into my Tascam DR07ii to act as a shotgun when I couldnt get close, with decent results.
The H4n is vgood, multi track with xlr inputs but may be expensive and more than you need, the H1n or Tascam DR 8 offer external inputs and good built in mics with probably all you'll need.
The syncing is easy enough in most decent editors, by zooming into the video & audio tracks, you can then drag the audio to coincide with an obvious event (eg, clap). The advantages apart from good clear audio are that you get a continuous sound track independent of video takes, meaning that you can cut to many different angles with good consistent speech etc. There are software available to automatically sync your tracks but I've found it easy enough in both Final Cut and Premiere doing it manually.