The ODM has a limited range. There is a limit on how long it can propel two hooks. Or just one, depending on what the user decides. But I do know there is a ton on inconsistencies, or there may not be, because the Scouts rarely grapple to the max, just to what's closest. 
right now this one is of Mikasa or Hange grappling to take out the Armored Titans eyes with thunder spears. What is the total range of the ODM gear?
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I don't know the max, but I do know that the ODM is less accurate, efficient and useful when used from a really far distance away. I can't remember if limited by wire length or grapple fire-power but either way, shooting from max range means the grapple will have lost its power and potentially not even break through the wood/brick, and thats if you even hit your target. You would have to use a lot more gas to jet upwards and keep yourself from sliding across the ground and when hurtling towards a single target really far away, the options for avoiding HITTING that objet become very limited.– JesseCommented Nov 5, 2019 at 3:54
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Yeah, those are some facts. We see people grapple long distances and stay there for a while. In season 2 Jean, Conny,Shasha and co go to find Eren but they find Yimir. (this is where she eats Historia) they don't regrapple they just fly. so i would assume they where grappling to somthng very far away.– xpertCommented Nov 5, 2019 at 13:33
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1 Answer
We can try to use mathematics here for a bit, which is definitely not a threatening way to start this answer.
This is a Mikasa figurine standing basically straight up, according to the wiki she is 176 cm tall (I'll do an imperial conversion of my final answer), in the picture she is 532 pixels tall, and the wire spools are 32 pixels in diameter, meaning the spools have a diameter of roughly 11 centimeters.
That feels a bit small to me, let's round that up to 20 centimeters and chalk the different measurement up to foreshortening.
The steel wire is coiled up inside of these circular containers, and here's where we'll get really mathy. I'm talking integral calculation mathy.
We're not going to bother with that though, instead we'll use this handy website that has a tool where you can just input the values.
It needs some values though, tape thickness (or in our case steel wire thickness) and the internal diameter of the spool/roll.
The above diagram suggests a tiny inner diameter, just a small gear, so let's estimate that at 1cm, and the wire thickness also at 1cm.
Let's insert those values (multiplied by 10 because millimeters are expected):
That's a range of just over three meters (or 10.29 feet), clearly wrong considering what we've seen in the show. Our estimates for internal diameter and wire thickness were already very generous though, and we "rounded up" the external diameter to 20cm.
Basically, the small drums we see can't realistically house the amount of cable we're seeing on the show. (Sorry)
But there's also no official source that specifies a maximum range I could find (otherwise I wouldn't have bothered with all of this, I assure you).
Maybe have a look at the longest shot they make in the show/manga and assume that that's about the furthest range? Though it might be hard to gauge the actual distance
(I don't recall any specific grappling shot falling short of its intended target (due to range), that would obviously be a far more helpful piece of information though.)
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I think I've said the longest shot they have made in the anime (i don't use the manga because it doesn't move) is in my comment above your question in the forest of giant trees.– xpertCommented Nov 5, 2019 at 15:36