Frontpage, being a Microsoft product, works best with other Microsoft products...so it's no wonder that the code from Frontpage would look fine in IE, but not in Netscape, Mozilla, or Opera.
IE is more forgiving when it comes to code that isn't 100% perfect.
Yes Frontpage does add it's own code, or should I say, it 'dumbs' down your code, adds extra tags, and adds IE-specific tags...tags that work in IE but not other browsers.
Frontpage is the absolute worst HTML editor on the market...the best is Dreamweaver MX...unless you are so awesome that you can just use notepad...Dreamweaver is not hard to learn, although different from Frontpage in it's look and feel...once you get the hang of it...it's very powerful. It supports everything from XML to plain 'ole HTML...it works with almost all server technologies...it's awesome. Dreamweaver will also help you design a page that will work in all browsers...
Buy Dreamweaver MX, pick up a book, and force yourself to learn it...once you've learned the basics of Dreamweaver, you'll laugh at yourself for ever having used Frontpage.
Frontpage is OK if you are just doing a basic site...with nothing but simple links...or you need simple site management...but as you learn more...you'll want a tool that can grow with you, and I think Dreamweaver MX is the way to go...