As Oscar Cabrero has already answered, you probably want a CDN and not true multisite hosting.

Static websites can be hosted on several continents with relative ease. Dynamic websites cannot -- replicating a (large) dynamic dataset (i.e. what is in your database) across slow and unreliable WAN links is a very hard problem to solve well.

So you want to keep all your dynamic content (i.e. your HTML generation) on one LAN, and move static content to a content delivery network.

Cloudharmony and Paessler have good tools to test and information about the CDNs out there.

Assuming you want to build a multisite dynamic website nevertheless:

Are there any pitfalls to watch out for?

Oh yes, many. Mostly in silent corruption of replicated data, or broken / stale / delayed replication.

Should I have separate domains for each area e.g. .com .co.uk etc

Completely up to you. If your sites are very regional / local in nature, then a local TLD may work best (i.e. .co.uk, .de etc).

Do I have a database per host?

At least one database server per site you're hosting from, yes.

How would I keep the databases up-to-date?

Your database engine's replication mechanism. Most databases have this. There are more complex solutions for high-end needs, but this is where you should start.

As Oscar Cabrero has already answered, you probably want a CDN and not true multisite hosting.

Static websites can be hosted on several continents with relative ease. Dynamic websites cannot -- replicating a (large) dynamic dataset (i.e. what is in your database) across slow and unreliable WAN links is a very hard problem to solve well.

So you want to keep all your dynamic content (i.e. your HTML generation) on one LAN, and move your static content (logo images, CSS, JS) to a content delivery network.

Cloudharmony has a test tool and some good blog entries about CDNs. Paessler has a performance overview and qualified CDN recommendations.

Assuming you want to build a multisite dynamic website nevertheless:

Are there any pitfalls to watch out for?

Oh yes, many. Mostly in silent corruption of replicated data, or broken / stale / delayed replication.

Should I have separate domains for each area e.g. .com .co.uk etc

Completely up to you. If your sites are very regional / local in nature, then a local TLD may work best (i.e. .co.uk, .de etc).

Do I have a database per host?

At least one database server per site you're hosting from, yes.

How would I keep the databases up-to-date?

Your database engine's replication mechanism. Most databases have this. There are more complex solutions for high-end needs, but this is where you should start.

As Oscar Cabrero has already answered, you probably want a CDN and not true multisite hosting.

Static websites can be hosted on several continents with relative ease. Dynamic websites cannot -- replicating a (large) dynamic dataset (i.e. what is in your database) across slow and unreliable WAN links is a very hard problem to solve well.

So you want to keep all your dynamic content (i.e. your HTML generation) on one LAN, and move static content to a content delivery network.

Cloudharmony and Paessler have good tools to test and information about the CDNs out there.

As Oscar Cabrero has already answered, you probably want a CDN and not true multisite hosting.

Static websites can be hosted on several continents with relative ease. Dynamic websites cannot -- replicating a (large) dynamic dataset (i.e. what is in your database) across slow and unreliable WAN links is a very hard problem to solve well.

So you want to keep all your dynamic content (i.e. your HTML generation) on one LAN, and move static content to a content delivery network.

Cloudharmony and Paessler have good tools to test and information about the CDNs out there.

Assuming you want to build a multisite dynamic website nevertheless:

Are there any pitfalls to watch out for?

Oh yes, many. Mostly in silent corruption of replicated data, or broken / stale / delayed replication.

Should I have separate domains for each area e.g. .com .co.uk etc

Completely up to you. If your sites are very regional / local in nature, then a local TLD may work best (i.e. .co.uk, .de etc).

Do I have a database per host?

At least one database server per site you're hosting from, yes.

How would I keep the databases up-to-date?

Your database engine's replication mechanism. Most databases have this. There are more complex solutions for high-end needs, but this is where you should start.