Getting the start note right is the important thing, and you can be thrown out by the acoustics of the room or the background noise or 1000 other factors. Two or three semitones out is not unusual for me, and it can be five or more! But depending on the tune it may not matter: When the Saints has a range of only a fifth, so if you can sing an octave and a half you can do it in all 12 keys!

Usually I can tell within the first bar or so if it's right or not, and can often "drift" the key down (or up) to the key I want. Unless some bastard decides to jump in with an accompaniment in the key I'm trying to escape from and locks me in!

One place where I sometimes have trouble is when I have learned a song from a single recorded source: I sometimes find that, despite attempts to transpose to "my" key, I have learned the tune in absolute, rather than relative pitch, and will reproduce the key of the source singer rather than my own. For instance, Mrs Costello's version of The Cruel Mother has a range of only a 6th, but I often start it in her key (an octave or two down) and end up singing it right down in my boots, struggling to reach the low notes.

It has also been mentioned above that your voice can change from day to day (or even hour to hour). My "comfortable" range is about an octave and a half from A to the D above the next A. But that A is not 440, it is the lowest note that I can comfortably hit at this moment without sounding growly. So a song that I think of as singing in D may actually be done in C or F tonight and still sound right because that's where my voice is right now.