Since you didn't show us desired output, I suspect your spec if faulty because what you show would not result in reasonable .html.

So, taking a guess (possibly wrong), if you're looking for this:

<p>Developmentally, 2-year-olds are generally more interested in thems
+elves, while dogs do care how their people feel, and instantly recogn
+ize a change in emotion.</p>

<p>"While your dog can't comprehend that you just received a traffic v
+iolation, he can tell that you're upset the second you walk through t
+he door," Coren says. "In fact, dogs can detect some subtle changes w
+hich even ad
ults can't," adds Coren. "We can't smell cancer or predict seizures, a
+s dogs can."</p>

<p>When I posted this story on my Facebook Fan page recently (<a href=
+"http://www.new.facebook.com/pages/ Steve-Dale/50057343596?ref=ts">ww
+w.new.f acebook.com/pages/Steve-Dale/50057343596?ref=ts, or simply ty
+pe Steve Dal
e into the Facebook search), I received some interesting responses:</p
+>

<p>Kelle: "Heck, my Italian Greyhound is smarter than most college stu
+dents."</p>
[download]

you could do this to the data you supplied (which, IMO, implies that you want to replace only those "<" which are followed directly by a space):

#!/usr/bin/perl
use strict;
use warnings;

my $output;
while (<DATA>) {
    if ($_ =~ /<.+>(<.+>)(.*)/){
        $output = $1.$2;
            $output =~ s/<!\[CDATA\[(.*)/$1/;
            # print $output;
    }
    print "\n\n";

    $output =~ s!(< )!</p>\n\n<p>!g;
    print $output . '</p>' . "\n";
}
[download]

But, as GrandFather said,

DON'T DO THIS!

There are too many corner cases, "gotchas," and other complications to make "rolling your own" profitable.