Things you must know before starting.

As you may find out you will need 3 of the DLCs, "The Zombie Island of Dr. Ned", "The Secret Armory of General Knoxx" and "Claptrap's New Robot Revolution". Since the other DLC "Mad Moxxi's Underdome Riot" has no claptrap rescue missions so it does not count towards collecting backpack SDUs. I really recommended buying the GOTY verson because it is much cheaper than buying all of it seperately and also in the sales it will only cost £4.99 for it.

Make sure when playing borderlands you can quit before saving. So first open up borderlands and start playing. Buy something of a vendor (something cheap). Soon after press ALT+F4 which closes the game immediately or press CTRL+ALT+DELETE then click on task manager and close borderlands. Wait a few seconds and then open up borderlands again. If it worked, the item you bought will not be there. You will use this method in acquiring some of the backpack SDUs in future.

Now I recommended you start a new character as you might of have messed up like me. If your new to the game, play as the siren since it is the easiest in my opinion to play and very helpful. She is very fast as she can use her action skill and speed for doing runs quickly, also she is very powerful as her primary weapon are SMGs and they are seen as the best for DPS in the game.

These claptrap rescue missions always involve finding a damaged claptrap then finding a repair kit and then going back to it for a chance to get a backpack SDU or grenade mod, XP and money. Sometimes the claptrap will even help you by locating a chest after turning in the mission.

Now when you first start playing you will be in playthrough 1. In this playthrough all the claptrap rescue missions you do will give a 100% guranteed backpack SDU as a reward except one.

There are technically 14 claptrap rescue missions in total (in each playthrough). Although the first one you do is part of the story but doesen't give you a backpack SDU as a reward.

The mission Claptrap Rescue: Lockdown Palace for some reason doesn't give you a 100% chance of getting a backpack SDU as a reward, instead sometimes it may give you a grenade mod. So by using the exit before saving method keep trying until you get it. By having a full backpack or even overloaded by mission rewards the chances of getting the backpack SDU seems to be higher but this still hasn't been proven properly so you don't have to do it. Make sure you don't walk near a save point after you get a grenade mod since the game will save and you won't be able to ever get that backpack SDU from that particular mission.

This is the list:

Mission names, locations and backpack SDU availability.
Claptrap Rescue in Fyrestone No
Claptrap Rescue: Safe House in Sledge's Safe House Yes
Claptrap Rescue: The Lost Cave in Lost Cave Yes
Claptrap Rescue: New Haven in New Haven Yes
Claptrap Rescue: Tetanus Warren in Tetanus Warren Yes
Claptrap Rescue: Scrapyard in Earl's Scrapyard Yes
Claptrap Rescue: Krom's Canyon in Krom's Canyon Yes
Claptrap Rescue: Trash Coast in Trash Coast Yes
Claptrap Rescue: Old Haven in Old Haven Yes
Claptrap Rescue: The Salt Flats in The Salt Flats Yes
Claptrap Rescue: Crimson Fastness in Crimson Fastness Yes
Claptrap Rescue: The Lumber Yard in The Lumber Yard Yes (DLC The Zombie Island of Dr. Ned required)
Claptrap Rescue: Lockdown Palace in Lockdown Palace Yes but not 100% chance (DLC The Secret Armory of General Knoxx required)
It's a Trap... Clap in Tartarus Station Yes (DLC Claptrap's New Robot Revolution required)

Now things are very different from playthrough 1 since only 7 (8 if you haven't done Claptrap Rescue: Lockdown Palace in the first playthrough) of the claptrap missions give you a chance of receiving a backpack SDU or a grenade mod (that we don't want).

First thing you must not do is complete the base game story in playthrough 2 (killing the destroyer), as this will give you a 0% chance of obtaining a backpack SDU or even a grenade mod in Claptrap Rescue: The Lumber Yard and It's a Trap... Clap. Make sure you do these two missions before doing Destroy The Destroyer as I made the same mistake!

This is the list:

Mission names, locations and backpack SDU availability.
Claptrap Rescue in Fyrestone No
Claptrap Rescue: Safe House in Sledge's Safe House Yes but not 100% chance
Claptrap Rescue: The Lost Cave in Lost Cave Yes but not 100% chance
Claptrap Rescue: New Haven in New Haven Yes but not 100% chance
Claptrap Rescue: Tetanus Warren in Tetanus Warren Yes but not 100% chance
Claptrap Rescue: Scrapyard in Earl's Scrapyard Yes but not 100% chance
Claptrap Rescue: Krom's Canyon in Krom's Canyon No
Claptrap Rescue: Trash Coast in Trash Coast No
Claptrap Rescue: Old Haven in Old Haven No
Claptrap Rescue: The Salt Flats in The Salt Flats No
Claptrap Rescue: Crimson Fastness in Crimson Fastness No
Claptrap Rescue: The Lumber Yard in The Lumber Yard Yes only if playthrough 2 story is not completed (DLC The Zombie Island of Dr. Ned required)
Claptrap Rescue: Lockdown Palace in Lockdown Palace Yes if not completed on playthrough 1 but No if already done on playthrough 1 (DLC The Secret Armory of General Knoxx)
It's a Trap... Clap in Tartarus Station Yes only if playthrough 2 story is not completed (DLC Claptrap's New Robot Revolution required)

If you did make the mistake of completing the story in playthrough 2 the only way of definitely getting the backpack SDU from those 2 missions is to go on a friends hosted game in which they did not complete the main story on playthrough 2.

Thank you dattebayo for the screenshot.

The legit max inventory space is 72.
An inventory of 42 spaces unlocks an achievement called "Fully Loaded".
Each backpack SDU gives 3 additional spaces to the inventory.
With more space you can have a larger collection of your weapons you would like to keep. With the bank from "Mad Moxxi's Underdome Riot" the total is 114. With the weapon, shield class mod and grenade mod slots this brings this up to 121.

If you have any questions, simply comment below.
What would be very helpful is if anyone can spot any spelling, punctuation and grammar for me to fix.

Hopes this helps and enjoy playing one of the best games ever!