This line, I think has a little problem.

If the first letter is a child of an “a” ancor, after swapping, the first letter will no longer be a child of the “a” ancor.

Did you use &lt; instead of < and &gt; instead of >? (see “IMPORTANT” above comment textarea.)

swap_letter();
	});
	function swap_letter() {
	  $('#content p').each(function(index) {
		var paragraph = this;
		var node = paragraph;
		while (node.childNodes.length) {
		  node = node.firstChild;
		}
		var text = node.nodeValue;
		var first_letter = text.substr(0,1);
		var match = /[a-zA-Z]/.test(first_letter);
		if ( match ) {
		  node.nodeValue = text.slice(1);
		  $('')
			  .text( first_letter )
			  .addClass('eerste-letter')
			  .prependTo( paragraph );
		  first_letter = "";
		}
	  });
	}

swap_letter();
	});
	function swap_letter() {
	  $('#content p').each(function(index) {
		var paragraph = this;
		var node = paragraph;
		while (node.childNodes.length) {
		  node = node.firstChild;
		}
		var text = node.nodeValue;
		var first_letter = text.substr(0,1);
		var match = /[a-zA-Z]/.test(first_letter);
		if ( match ) {
		  node.nodeValue = text.slice(1);
		  $('')
			  .text( first_letter )
			  .addClass('eerste-letter')
			  .prependTo( paragraph );
		  first_letter = "";
		}
	  });
	}

		  swap_letter();
				});
				function swap_letter() {
				  $('#content p').each(function(index) {
					var paragraph = this;
					var node = paragraph;
					while (node.childNodes.length) {
					  node = node.firstChild;
					}
					var text = node.nodeValue;
					var first_letter = text.substr(0,1);
					var match = /[a-zA-Z]/.test(first_letter);
					if ( match ) {
					  node.nodeValue = text.slice(1);
					  $('')
						  .text( first_letter )
						  .addClass('eerste-letter')
						  .prependTo( paragraph );
					  first_letter = "";
					}
				  });
				}

CSS

#content .eerste-letter
font-size:2.5em;
line-height:90%;
padding-right:3px;
text-transform:uppercase;
}