Otdfbt

The context of this sentence is that I know that I had asked before what the departure time is of the train that my friend was going to take. Unfortunately I had forgotten it, so my brain decided that a past tense would make sense and ask:

"When was your train leaving?"

instead of

"When is your train leaving?"

Is using the past tense in this situation correct and/or common?

You can, actually, use the past tense to ask a question about the future, but it's not really that simple.

"When was your train leaving?"

What is implied here is that the person asking the question knew or was told the answer to the question but forgot. It's often a shortened form of

"When did you say your train was leaving?"

So the question really is about an event that happened in the past—involving the discovery or relation of the information about the train leaving—which has a bearing on the future. It is not a direct request for information about the future event, except as filtered through past events.

This is actually a great question. Robusto's answer is perfect, but there are other times when you'll hear speakers using that manner or "style" of speech where it doesn't fit the scenario described.

For example, say you walk up to a newsstand and ask for a newspaper. The clerk doesn't respond and just goes back to playing a game on his phone. You might stand there for a bit in disbelief, then say, "So, were you going to get me that newspaper?"

All native speakers recognize that use of the past tense for an event that hasn't occurred. In this case, it carries the message that you think it should have been done already. You are conveying irritation, but in a grownup, I'm-making-a-conscious-effort-to-be-civil kind of way, and, possibly, sprinkled with a little uncertainty as in, "Is there something here I'm missing?".

Another variant of your question that I've heard (although replace train with plane). Say someone woke up too late to travel to the airport to make their flight (which won't depart for some 30 minutes), and they told you this, you may say:

When was your flight?

Which should probably be interpreted as a truncation of:

When was your flight scheduled?

or

When was your flight meant to be?

When was your train leaving?

Might give the response:

10 o'clock, same as before :)

(The implication being, that you thought it was leaving at 9, but now it leaves at 10).

or:

It hasn't left yet.

Unfortunately I had forgotten it ...

OK, so say that:

I've forgotten what you told me. When is your train leaving?

or:

Can you remind me when your train leaves?

We usually ask "when was" if there has been a change to the schedule or the time has passed, even if the event has not occurred. The meaning here is that in the past the time of a future event has changed.

"So when was your train supposed to be leaving."

But we can use also use it if we consider that the reply is not authoritative :

"So when did you think the train was leaving?"

Although is is discourteous to suggest you doubt their word in a dismissive manner.

These usages are common in Airports, Taxis, Train Stations and Bus locations.

Writing as an incorrigible pedant I dislike both. I would say:

"When does your train leave?"

or

"When is your train going to leave?".

I cannot think of a reason to reject "When will your train leave?" and would happily use it myself but it seems not to be commonly used and may be considered odd.