If you want to record any video content played in your browser you can use Snow Leopard's QuickTime X screen recording feature. If you want to avoid the need for cropping the video, put the video on full screen before starting the recording.
If you also want sound with your video you need reroute the speakers to the microphone with a software like Soundflower and select this new input source within Quicktime X as an input source for sound.
The fastest way to browse your directories in OS X is clearly the column view that you access by pressing Apple-3.
However in this view long file names are usually partially hidden, which can be a problem. Worry not, there is an easy way to resize the width of these columns. Just drag the separator line at the little handle at the bottom. This operation will only change one column at a time.
You must have noticed an annoying little bug in Snow Leopard. When you try to open multiple files it only opens one at a time. Unfortunately I couldn't find a perfect solution, but there is an intermediate workaround until Apple fixes it.
Just a quick word of caution. If you need the extensive export features of Quicktime Pro, make sure you backup the application before upgrading to Snow Leopard 10.6. Snow Leo overwrites your old QT and will offer less options. After the installation you can simply move back the Quicktime 7 application into a different folder or renamed to differentiate from the new version.