When operations don't go as planned, what should one do, find the error and correct it or start all over from scratch?

it depend on the situation, you can’t just start over from scratch, in all cases you need to find out the cause and then act.

You need to know how big the problem is, and what does it take to resolve it, unfortunately this is not so obvious in many industries, where you are able to see what is wrong, and fix it immediately.
In many industries that I have seen, you sometimes get to the dilemma of reworking vs starting over, where reworking may take more than starting over in some cases.
The magnitude of the issue, the complexity of the project, and the delivery quality and reliability are the first aspects to consider, is the issue too big to be fixed? (let's say you are fixing a structural damage for an aircraft wing, and the method you are using is not working, it's obvious you'd start over, as fixing it will highly affect the quality of work, as however, for a seat that is not reclining, you'd want to do minor fixes, and you would not be concerned if occurred again after a while before changing the seat).
Another aspect to look into, is how visible is this fault, in the end, an organisation/contractor wants to be seen successful, and does not want to have cynical customers, that is why you do not see many aircraft development programs suspended, and most recent projects run way off budget and schedule, as the initial design was not carefully considering some aspects (electrical wiring in A380 for example).

I wouldn't recommend to start from scracth anything without checking and analysing the problem that caused the issue.
If you don't know what is the source of the problem how you can be sure that you won't make the same error in the future though you have rebuild something from scratch.
To make mistakes is normal.
It's part of our life.
But as a good manager and a vise man you should learn from these mistakes and assure you are not making them twice.

In life we learn from mistakes so it is very important that we find our errors,  understand how we made them.
Rectify the error, learn from it and move forward.
It doesn't however mean we have to start from scratch unless the error was such a catastrophic failure that the whole process needs to be rethought and executed differently..

Coneptually, the answer is to define the problem, identify the alternative solutions, and then work with th management to decide on the actions to solve the problems.

I see that an operations plan is a plan to best use your resources (financial and otherwise) to supply the targeted demand.

If the problem is within the targeted demand, then you might have an eroneous forecast, or an unaticipated change in the economics of your line of business in the targeted markets.

if the problem is within your supply, then you might have a problem in your acquisition of raw material, performance of your human asset, or your production capacity.

Ech of these situations have different techniques to handle it. But in any case I don't think that any of us have the lesure of starting anew.

In logistics errors need to be corrected while work is going on and there is no time to start from scratch at the tactical day to day activities level.
Things can be overhauled and started from scratch at strategic level but at the tactical level you need to incorporate changes on the run.
For example delivery route planning changes can be done on a daily basis at the tactical level.
At the strategic level changes to delivery modes and transport modes can be made and implemented in the long run. 

It would not be wise to start all over again from scratch.
This way you are loosing an opportunity to learn from your mistakes.
Moreover, error may be small or big but is likely to creep up again without you immediately knowing it.
Keep the operations ongoing and divert a part of the energy to locate the error.
Do a root cause analysis and get to the bottom of the fault.
This way you can find ways of eliminating it and avoid it's recuurance.

without alocating the error, the probabilities of being repeated over and over is huge.
finding the error radidly through deviding the process into larger parts than what was set as targets before.
this will provide fast error locating.

Depending on the type of error if it is a Major Error in this case you should start all over from scratch but if it is a Minor Error in this case you can correct it and there is no need to start from scratch. 

find the error, meagure the deviation, analysis that deviation, then take the action.

Offcourse, the whole plan shall be thoroughly scanned to uncover problamatic areas, necessary adjustments (corrections) shall be proposed and implemented.
 Subsequently, newly implemented adjustments shall be strictly monitored and re-adjustments shall be proposed if necessary.
START-OVER SHALL NOT BE CONSIDERED AS IMMEDIATE SOLUTION UNLESS VARIOUS AVAILABLE ADJUSTEMENTS (CORRECTIONS) ARE TESTED....
SIMPLE START-OVER MEANS WASTAGE OF EFFORTS (BOTH TIME & COST) UTILIZED SINCE BEGINING