With spread bets and most futures contracts the only way you’ll see dividends is when they are reflected in the share price. Before a dividend is due to be paid the share price rises and after the dividend has been paid the share price falls. This is not the case with Contracts for Difference.
A Contract for Difference covers the total return from an instrument, which means that if there is any income from the instrument this is added to the difference. If you are holding a CFD with a long position when the equity dividend is paid out then the provider of the CFD should pay credit the dividend to the amount they owe (or subtract it from the amount you owe them). This is offset against the interest that is payable to the provider.
The bad news is that if your CFD is short on an equity then your position is adversely affected by the dividend being paid. This is unlike (at least directly if not indirectly) shorts that are done through spread bets or futures. However as interest is being paid by the provider then this is offset to some extent.
Corporate actions, as they have an effect on the return also affect a Contract for Difference. This means that if there is a rights issue and there is a value on the rights then these will be sold and the value added or subtracted to the CFD position.
The tax treatment of this is unusual, in that it will all be treated in most countries as Capital Gains Tax rather than dividends. This can be advantageous for UK higher rate tax payers as they are paying a lower rate on CGT, and have a generous exemption, particularly if they are married.