Missions & Complexes

On the other hand, a player scanning down a mission and then swooping in to swipe the mission critical item... only to then ransom it back to you is part of gameplay.
I've had it happen to me. I've done it to others.
Missions aren't instances with barriers that automagically keep others out while we nom on red crosses to our heart's content, and I'd be willing to bet good iskies that the gm's would likely take a dim view of dishonest petitions sent in to circumvent the inconvenience another player levied on you.

Edit:
If something like this does happen to you, you do have a few options available to you though. One is to try and negotiate with the person who took your item, they may be willing to trade it back in exchange for a ransom.
Another is to accept the loss of the mission and move on. It's not ideal, but it's safe... it'll cost you a standings hit with the agent in question and I think a lesser one with the corporation they work for.
Or you can engage this individual in a holy trial by combat.... if you win you've got an estimated 50% chance that your mission item will be in the wreckage. However, as Ilshira has pointed out, this can be a risky venture as this may be exactly what your erstwhile foe wants.

This reminds me, I should probably put some of those up for sale and get paid for my time at least.
Not the damsels though, those bitches be mine.

So what is the easiest way for me to find out what the desirable mission items are? Just, um, out of interest.

I hope the answer isn't to do all the missions!

I had a player join me whilst doing a mission, it was quite funny watching him try and upset me. Best thing to do is ignore them until they warp off feeling totally impotent and defeated. If they do take the mission critical loot just drop the mission and take the next, it's not like there is a finite number of missions.

I had a storyline objective taken a couple years ago. My mission ship didn't have enough cargo space for it so I jumped back 3 systems for a hauler. By the time I got back, the objective was gone and a flashy cross was sitting there.

I said, "well played, you got me there". He offered to sell it back. I said, "Sure, how much." He docked up and logged off.

I petitioned and was basically told, too bad, so sad. Failed the mission, took a pretty steep hit to standings and continued to grind standings. As if I wasn't going to do it anyway, right?

I also moved mission hubs and haven't seen an interloper since. (dscan, dock up, etc.)


So, TLDR
Don't expect the mission to be reset if your objective is taken.

While I'm sure you are correct, I will bring to attention which mission the OP was having trouble with and please note it is no such arc mission.

Shoot the wrecks... That's what I normally do.

When I level 4 mission, I will use my directional scan to search for combat scanner probes. You need to do the same.

Combat scanner probes are what you use to scan down another player's ships, that's what you have to look out for; core scanner probes just scan down various signatures. Adjust your scanner range to get an idea of how far away the scanner probes are to your location. If at least 4 of them are within 4 AU, it probably means YOU are the one getting scanned down. It is time to dock up.

At one point, I was doing a longer mission (Angel Extravaganza maybe?) and those combat scanner probes kept trying to land on me. I kept docking up. It was back and forth for a while, but eventually the ninja looter was forced to look for somebody else.

As has been said before, do not engage a ninja looter in a pve ship.