It really depends on the HA system you're using.
For example, if your system uses a shared IP and the traffic is managed by some hardware box, then it can be hard to determine if a certain box is a master or slave. That will depend on a specific solution really... As long as you can add a custom script to the supervisor, you should be ok - for example the controller can ping a daemon on the master server every second. In the alerting script, simply check if the time of the last ping < 2 sec...
If your system doesn't have a supervisor / controller node, but each node tries to determine the state itself, you can have more problems. If a split brain occurs, you can end up with both slaves or both masters, so your alerting software will be wrong in both cases. Gadgets that can ensure only one live node (STONITH and others) could help.
On the other hand, in the second scenario, if the HA software works on both hosts properly, you should be able to obtain the master/slave information straight from it. It has to know its own state at any time, because it's one of its main functions. In most HA solutions you should be able to either get the current state, or add some code to run when the state changes. Heartbeat offers both.
I wouldn't worry about the edge cases like a split brain though. Almost any situation when you lose connection between the clustered nodes will be more important than the stuff that happens on the separate nodes :)
If the thing you care about is really logging / alerting only, then ideally you could have a separate logger box which gets all the information about the current network / cluster status. External box will probably have better idea how to deal with the situation. If your cluster gets dos'ed / disconnected from the network / loses power, you won't get any alert. A redundant pair of independent monitors can save you from that.
I'm not sure why you mentioned DNS - due to its refresh time it shouldn't be a source of any "real-time" cluster information.