Seaport said:
First question, if my pages pass the validation, what does this mean? Does it mean that my pages will work on all major browsers?
No, it is possible IE might still wander on its own.
Seaport said:
I intend to make my pages work on IE, Firefox, and Netscape (if possible). Will this validation service help me on that?
Which Netscape? It is no use giving too much support to v4 (apart from letting people see the content) and v7 is the same as FF. So as soon as you support one, you support the other. NN6+, Mozilla and FF are all based on the same rendering engine -- Gecko.
Yes, validation service will help.
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Validation service will alert you of the first and foremost thing you need to have when designing modern websites -- a doctype. As soon as you have the doctype, validation service will help you maintain a correct code but more importantly, your pages will force standards-compliance mode in browsers. That will ensure a better cross-browser compatibility of your pages.
Currently, your pages work in IE but not if FF. I think I am safe in assuming you are not using a complete and valid doctype. As soon as you will put one up, IE will break almost as bad as FF and you can start fixing things. Validation service will help you to extent not to make silly mistakes that might or might not interfere with how the page is rendered. It will warn you about tags that are not closed, improperly nested tags and a lot more. All these things can contribute to a page not looking correctly in different browsers and having a valid page greatly reduces chances of that happening. However, with IE's sketchy support and years of browsers following their own set of rules as opposed to commonly accepted standard it is difficult to get the page look the same across all browsers. The standards employed at W3 (the consortium that is providing you with the validator) are by all means very welcome, but some of the browsers are still having trouble incorporating them into their rendering engines. So...
It is possible to have a completely valid code that will render widely different on different browsers due to browsers' support or lack of for certain features. Sometimes it is also a case of different interpretation of certain features. So it is unfair to say that valid code will be rendered the same across all browsers. However, it will greatly increase the chances it will be. The rest is determined by the complexity of the code.