I think using OT servers would be an improvement over the existing model for both currency and share exchanges. This could spring more specialization and provide more security. The current exchanges and eWallets would be issuers and the proper exchanges would reside in OT servers with less critical security. If there's enough of them, you only really need to trust the issuers.
But is worth to consider the idea for a longer run.
The advantage of the chain solution is that it would enable a global and completely decentralized market, but it has disadvantages too.
For example, the trades in OT are instant, but the trades within the chain may take longer.
The simplest design I can think of would be a chain like bitcoin but in which each key pair can issue its own currency.
Each output would need to additionally contain the address of the issuer.
The units can represent anything: an mtgoxUSD, a property tittle, an Islamic Bank of Bitcoin share, a right to vote in your neighbor assembly, an IOU for an hour of work...
The parties involved are responsible to make good for the property represented outside of the protocol.
For example, you can pay back your tradehillUSD to tradehill to receive the funds in your bank account.
To receive the profits of a share, you can sign with the key that holds the shares the bitcoin address you want to receive them on.
Basically it would work like smart property but without the need of the "tainted satoshi".
This has an advantage. Some transactions are "instant".
For example, If I give you 10 fresh issued timonCoins, you don't really need to wait for confirmations once you have the transaction.
There's no way I can double spend something that I can just create at will. When you give them to a third person, he has to wait because you can cheat him by doublespend.
When I issue and give them to you I can cheat you, but I don't need to double spend. I can just not honor my word as you're directly trusting me when you accept my shareCoins in exchange of something else.
The fees can be payed in bitcoins or the tokens within the chain (but some miners may not want them).
With contracts the tokens can be securely traded for bitcoins.
Trade tokens between them is trivial (like trading a tainted satoshi for regular bitcoins in the smart property wiki page).
Maybe an additional communication protocol to send messages directly to a given address would be useful.
For example, when the manager of a company wants to pay the dividends, he can look the public keys of the shareholders and send them a ciphered message asking for the bitcoin address.
I have no clue how this could work for options though.
As an aside, maybe it should be called more generally a Distributed Asset Exchange since Bitcoin is just the currency of choice and Stocks are just one instrument that might be handled within it.