What are the allowed tags inside a <li>?
Solution 1:
TL;DR: an <li> can contain any element that is valid in <body>.
In the HTML 4.01 spec for lists you’ll find the relevant extract of the DTD:
<!ELEMENT LI - O (%flow;)* -- list item -->
This specifies that an <li> may contain flow content, which is the collection of all block and inline elements.
The HTML5 spec for an <li> is the same in that it also allows any flow content.
Solution 2:
It's a block level element so pretty much anything goes. Trouble only comes when you're putting block level elements inside inline ones.