First, let me recommend that you go get Office SharePoint Server 2007 Administrator's Companion and spend a few nights/weekends reading it cover to cover. Next, pick up Beginning SharePoint 2007 and spend some time going through the examples. Both of these books are valuable to both a SharePoint administrator and the second book will give you a good perspective as a site collection owner/site manager.
As for online training, there are multiple blogs that have excellent information doing normal everyday tasks. Try Mark Miller's (a forum participant) blog or Bob Mixon's blog. You can also find useful information on the Microsoft SharePoint Team blog. You can also get training from Microsoft's eLearning site that is web based and affordable. Finally, there are several individuals out there that can do workshops or online training.
Unfortunately, there is no "shortcut" way to learn SharePoint. Many of us have been going through "trial by fire" as we learn this platform, and we'll all be glad to share our war stories with you. However, the benefits of training and learning this system far outweigh the time. The nice thing about SharePoint is that your end users really don't need as much in-depth training. They mainly need practicle "HOW DO I DO THIS" training.
As for the error with IE, I experienced this a lot prior to rebuilding my machine. This was because of all the junk that I installed over time on the computer, and I ended up trashing some of the AJAX components -- several of which control the menus and other items in SharePoint. I have had these problems before using both IE 6 and IE 7, so it's not the version of the browser that is causing the issue. I knew I had a problem when I went to check my web-based email using an AJAX enabled email site (Yahoo). When it crashed, I knew it was time to rebuild the computer. I've had zero issues since.