There are cases where explicit tags help, but sometimes it’s needless pedantry.
Note that the HTML spec clearly specifies when it’s valid to omit tags, so it’s not always an error.
For example you never need </body></html>. Nobody ever remembers to put <tbody> explicitly (to the point that XHTML made exceptions for it).
You don’t need </head><body> unless you have DOM-manipulating scripts that actually search <head> (then it’s better to close it explicitly, because rules for implied end of <head> could surprise you).
Nested lists are actually better off without </li>, because then it’s harder to create erroneous ul > ul tree.
Valid:
<ul>
<li>item
<ul>
<li>item
</ul>
</ul>
Invalid:
<ul>
<li>item</li>
<ul>
<li>item</li>
</ul>
</ul>
And keep in mind that end tags are implied whether you try to close all elements or not. Putting end tags won’t automatically make parsing more robust:
<p>foo <p>bar</p> baz</p>
will parse as:
<p>foo</p><p>bar</p> baz
It can only help when you validate documents.