If I buy VUSA from one exchange, can I sell it in a different exchange, assuming my brokerage account lets me trade in both exchanges? Or is it somehow tied to the exchange I bought it from?
This doesn't happen for all securities and between all stock exchanges. So that is dependent on broker and country. I checked for VUSA with Selftrade. They categorically refused allowing me to trade in VUSA in different exchanges. I can only buy and sell in same currency only, albeit sell(buy) in the same exchange where I buy(sell) from. Should be the same behaviour for all brokers for us mere mortals, if you are a bank or a millionaire than that might be a different question.
The VUSA you quote is quoted in GBP in LSE and in EUR in AEX, and the ETF has been created by an Irish entity and has an Irish ISIN.
As Chris mentioned below, happens between US and Canadian exchanges, but not sure it happens across all exchanges. You cannot deal in inter-listed stocks in LSE and NYSE.
Since it's the same asset, its value should not vary across exchanges once you compensate for exchange rates, right?
Yes, else it opens up itself for arbitrage (profit without any risk) which everybody wants. So even if any such instance occurs, either people will exploit it to make the arbitrage profit zero (security reflects the equilibrium price) or the profit from such transaction is so less, compared with the effort involved, that people will tend to ignore it. Anyways arbitrage profit is very difficult to garner nowadays, considering the super computers at work in the market who exploit these discrepancies, the moment they see them and bring the security right to the zero arbitrage profit point.
If there's no currency risk because of #2, what other factors should I consider when choosing an exchange to trade in? Liquidity? Something else?
Time difference, by the time you wake up to trade in Japan, the Japanese markets would have closed. Tax implications across multiple continents. Law of the land, providing protection to investors. Finding a broker dealing in markets you want to explore or dealing with multiple brokers. Regulatory headaches.