what happens if one set id attribute values of several html tags, the same string?

Question

I recently saw a html page, that i thought the id of several html tags was the same, then I realized the ids are unique but it raises the question that what could have happened

Answer 1

Change them as soon as possible, to save a lot of headache in the future. For elements with same property use classes

About your queries,

Now i wonder what happens if it is not the case??
Well, the HTML is not a valid one anymore. Now a days it doesn't hurt much but still not preferred.

What possible errors can it cause?
Errors are little bit hard to predict. But with jQuery you are going to get many.

Does different browsers show different reactions for this issue?
Not sure.

Does javascript and jquery codes that use duplicated ids run on both tags or what?
jQuery will give you trouble. Consider a case where you have two input fields with same ID. and you try to select second one with out noticing. jQuery('yourID').val() and you'll be selecting the firs value instead. Like this there are a lot of possibilities.