some really useful advice here already I think, definitely Sleepy Rosie's mental exercises and recording yourself.

I know it can be traumatic listening to your own voice from the outside as it is often nothing like you hear inside your head (a lot of which is to do with internal resonances inside your skull, I'm told) plus we're all often our own harshest critics... but if you can bring yourself to do it, it can be extremely valuable as a tool. Also don't forget that if you're recording on a little portable device (which is convenient and really all that's needed) you're not going to get the sound quality of a studio recording, so don't judge it too harshly on that front.

Another few thoughts of my own, which may or may not help. Apologies if others have already said these...

1) there's often a particular jump in a melody where the key shift happens. If you analyse the song and work this out, then you can just practice that interval for a bit (along with an instrument if that helps) to get a 'muscle memory' of producing that interval accurately. Recording yourself may help work out where the slip is happening.

2) I've got a chromatic tuner (circular blow pipe thing with a single reed for each note, you just blow into the little hole for that note, dead easy to use and mine cost £8) which I find invaluable for finding start notes.

3) Practice one verse at a time, or even one line at a time, with playing the start note on an instrument (or in my case, the chromatic tuner), then singing the verse/line then checking the end note. Repeat ad infitum.

4) Relax. I'd agree with others who say that a bit of slippage is not the end of the world - it's the overall delivery of the song that your audience is going to be listening to. BUT that said if you're a bit of a perfectionist and want to make sure you don't slip, don't be put off from working on it!