Add  link around each row in views
I usually remove all default formatting from every field, then hide all of my fields from display apart from the last field in views, and also remove all formatting, making the hidden fields plain text where possible.

Then in that last fields settings, rewrite the results, and input all of the fields as tokens from the replacement patterns.

Then instead of div elements, I use span which plays better inside an anchor, and just add unique classes for each span element.

So an example rewrite results might be...

&lt;a href="[path]"&gt;
&lt;span class="title"&gt;[title]&lt;/span&gt;
&lt;span class="body"&gt;[body]&lt;/span&gt;
&lt;/a&gt;


This should not suffer the same issue if you go to each hidden field, and under the style fieldset, make sure than no default wrapper or classes are applied, and also that each field is plain text. This will strip all formatting and place it inside the rewritten span elements. Like @BeeBee says, div and p will break the anchor wrapper.