What is the performance impact of indexing a frequently updated column?
Surely READ UNCOMMITED is a recipe for disaster? It's not called "Dirty Read" for nothing!

Everything I've ever read about Oracle says so. In particular, Tom Kyte's "Oracle Database Architecture" which flat out states that Oracle refuses to provide that level and that is a good thing! 

I saw the MySQL tag on this post, but this is universally applicable to databases in general IMHO.

Of course indexes slow down INSERTs and UPDATEs. Also, naturally, they will speed up SELECTs.

You can't know in advance performance will be affected for either case except by extensive experience and/or testing. What to do about this is a business decision, not a technical one. 

Your question cannot be reasonably answered without far more information. Your UPDATE queries? Your SELECT queries? Your transaction rates? Your disk setup? How are your iostat results? Your entire sar statistics? Is your system humming or do you experience bottlenecks/slowdowns?

How is your budget? How much of a delay in reporting can the business tolerate? My first instinct in your case is to go for an offline data-warehousing solution with a 24 hour lag (DW built overnight - using some form of replication). 

This is from my experience of how OLAP reports can cripple a running OLTP system. However, I cannot say for sure without far more information.