This is the line where it goes wrong:    
$backtrace = debug_backtrace();

In the php error log i also see references to line 1895 of engine/lib/entities.php ( referer: http://www.aabbcc.com/pg/groups/world/) with runaway (30sec) tasks. That line is:
elgg_deprecated_notice('get_entities() was deprecated by elgg_get_entities().', 1.7);

Ok, so what i wrote earlier was totally nonsense :-( except for the part that it has something to do with changes in 1.7.1b

Old:
function friendly_title($title) {
    $title = trim($title);
    $title = strtolower($title);
    $title = preg_replace("/[^\w ]/","",$title);
    $title = str_replace(" ","-",$title);
    $title = str_replace("--","-",$title);
    return $title;
}

New:
function friendly_title($title) {
    return elgg_view('output/friendlytitle', array('title' => $title));
}

This is called in the start of flexgroupprofile in the case that the Profile Format = default and never returns. If i put in the old part in the new elgglib then it works again.
I can't figure out why though!

Anything more response on a fix for this problem?

No, because no one else has reported this problem.

OK... Can I report the problem then?

I was getting the "PHP Fatal error:  Maximum execution time of 30 seconds exceeded" error in the log and then a blank screen each time I tried to access a group. If I turned off the FlexGroupProfile addon, everything was back to normal.

I modified the friendly_title() function in the "engine/lib/egglib.php" file as Ruben suggested... and everything works again. Guess it has semething to do with the Title?

Elgg 1.7.1
FlexForms 0.87 (I think?)

Weird. As flexprofile has nothing to do with the 'output/friendlytitle' view and I can't reproduce this problem, I can't help.

If you figure out what is wrong, please post it here.