What's wrong with this flashing code?

[Jolten]

You've simply got the tags wrong.

You have:

<if condition=="">
stuff
</if>
<else />
<if condition="">
</if>

What you need is:
<if condition="">
stuff
<else />
<if condition="">
stuff
</if>
</if>

The basic structure is <if> blah <else /> blah </if> If youwant to embed an conditional with in the else statement then it needs to be self contained so <if> blah <else /> <if>blah</if> </if> but the wrapping conditional needs to still maintain the same structure.

  <!-- nav buttons bar -->
<div align="center">
<table width="30%" cellpadding="0" cellspacing="0" align="center"><tr>
<td><img src="$stylevar[imgdir_misc]/mem_left.gif" alt="" border="0" /></td>
<td width="50%" class="membersbar">
</td>
<td width="40%" align="center" class="membersbar">
<if condition="$show['pmstats']"> <phrase 1="$vbphrase[unread_x_nav_compiled]" 2="$vbphrase[total_x_nav_compiled]" 3="$session[sessionurl]">$vbphrase[private_messages_nav]</phrase>
<else />
	<if condition="$bbuserinfo['pmunread']"> 
      <img src="$stylevar[imgdir_misc]/pmalert.gif" alt="" border="0" />
    </if> 
 </if>
</td>
<td><img src="$stylevar[imgdir_misc]/mem_right.gif" alt="" border="0" /></td>
</tr></table>
</div>
<!-- / nav buttons bar -->