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What is an appropriate UML diagram if I want to display how user request web page, enters some data, then posts the form (and if the validation has not succeeded, user is redirected back to requested web page)?

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That would be the sequence diagram (see also message sequence chart) in which you represent the success and failure as separate parties.

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If you want to represent the sequence of calls in a system to perform a specific functionality then use sequence diagram or If you want to describe the general sequence of actions for several objects in several use cases then use Activity diagram. sequence diagram may also express conditions, loops and concurrency by using guards, but they are not as intuitive and convenient as those in activity diagram.

As per your description you have to use sequence diagram.

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