Is there a program or anything that will look for any problems in a large familySearch tree?
Short Answer: 'Yes'.
There are now a few programmes/applications that one can use ...
Many are available through the "Solutions Gallery" in 'FamilySearch':
A selection of just some ...
▬ (BYU) Tree_Sweeper
From: Brigham Young University; Family History Technology Lab = https://familytech.byu.edu/
Have you ever found that a particular ancestor was born before their parents? Tree Sweeper will help you to find unlikely or erroneous parts of your tree and will help you to fix them.
Go to "TreeSweeper": https://treesweeper.familytech.byu.edu/start
The "Puzzilla", Descendants Viewer, is a combination of free basic services plus subscription premium services that help researchers see descendants in "Family Tree", of 'FamilySearch', using compact symbols that reveal patterns of incomplete research and other work in collateral-lines. Names and details appear as you move the pointer over the symbols.
Through the "Solutions Gallery" in 'FamilySearch':
▬ Find_A_Record ... "Browser" Extension (eg. "Chrome" Extension)
Connect your FamilySearch tree to the Find-A-Record Research Assistant.
Quickly connect your FamilySearch tree to Find-A-Record.
Find-A-Record scans your Tree and generates genealogy research opportunities. Opportunities include missing birth or death information, record hints, missing parents, possible missing spouses or children, data problems such as being born after you died, and poorly formatted information. For Member of the Church it also generates opportunities relating to "Temple" Work
"Kinpoint" makes it easy to do Family History by providing a customized experience, focused on what matters to you. Quickly find missing information in your family tree and discover insights into the lives of your ancestors.
There are more.
I hope, that some of these may help/assist, somewhat.
Related post ...
'Category' = Family Tree
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Is there a program or such, that can detect any problems in a large family tree on FamilySearch?