Round the world ticket or multiple one ways?

[kazino]

Have a some travelling to do and it got me thinking a round the world trip might work out better than booking one ways.
 
My itinerary is london, Orlando, Los Angeles, Hong Kong, Bangkok, Rangoon, Mumbai, Dubai, Muscat, London. 
Usually I would not be going to Los angeles so would just do a return from London to Orlando and then a return from hong kong via emirates (with the return leg from dubai rather than hong kong) and book some of the in between flights as one way tickets. 
But since I'm going to LA thought a round the world might be a better and cheaper option. I would need the dates to be flexible (don't mind paying a fee for changes). 
If not round the world I was thinking to just book one way tickets for each leg of the journey. 

[Puggit]

You need a travel agent. There are some strange quirks to your trip in that you are going the wrong war around and I suspect the number of stops might be too many,

[sneijder]

Depending on the airline, they're within their rights to demand to see a ticket out of Thailand and Dubai before they'll let you travel.

[firman]

We used these guys, http://www.roundtheworldflights.com/RTW-round-the-... for our multistop tickets. We paid £900 for the flights + £600 in taxes and that was London - India - Vietnam - Singapore - Thailand - Australia - New Zealand - U.S.A - London

[kazino]

Thanks chaps, is it worth trying the mainstream travel agents aswell - Expedia, southall travel?

900 + taxes that seems like a decent amount.