My two cents

IMHO, Online mall hosting platform and Orkut like engine are my choices
among your ideas.....

Why ? Because, I have the least idea about :-
=============================================
1)Real-world-event scheduler
2)Flat file join tool in perl (Richie, dont laugh)
3)Web crawler, scraper etc
4)Apache log analyzer.

And Blog Platform is about updating some file and later publishing as HTML.
The file format might be creepy.Here you may have sophisticated
parsing routines to check whether the user has entered a proper
html document or screwed up some tag in the middle etc..those kinda things...
(I am curious about how you will register
domain names....for eg. how will you register .blogspot.com as a site inside
your main site.)

But consider Online Mall Hosting Platform & Orkut like engine.
================================================================
->U can use apache for web server

->U can use xml and give an RSS/Atom link for mall hosting platform
to post "WHAT's NEW?" products.
(Btw, the link for this site's feed is
http://alpha-q.blogspot.com/atom.xml)

->U can change the requirement-specs 200000 times and use all the other
technologies you have mentioned....
But the challenge is to use filesystem at the back rather than Oracle or
SQL server..Thats when you gotta sit in front of your comp,
until your @SS becomes numb.

chow..
will try to get some ideas .....(if an idea flashes,that is)