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I think of MSDS (now SDS) as documents of external origin. As such, the organization is not responsible for controlling their revision (content) but is expected to provide up-to-date information to personnel as needed. What do your procedures say about them? ISO 45001:2018 requires (7.5.3) that "Documented information of external origin determined by the organization to be necessary for the planning and operation of the OH&S management system shall be identified, as appropriate, and controlled." Are SDS necessary for the planning and operation of your OH&S management system?
There were good reasons for MSDS to move to their new format. They used to be so different - some needed a PhD in Chemistry to understand, others left out large sections of information and said "proprietary." The new format is not perfect, but I think it is an improvement.
The task of keeping these up to date is thankless, and can be enormous depending on the number and type of chemicals you have. Some manufacturers provide a copy of SDS with every bulk shipment, while others must be researched on line or requested by telephone. This can become awkward as manufacturers go out of business, are acquired, change their names etc.
As an auditor I have issued nonconformances for failure to keep these documents current, but largely did so if the organization claimed to have control of it and I found truly ancient MSDS... I am talking about 1992 vintage. A lot can change in that much time, based on updated medical understanding of effects some of these chemicals can have.
As far as checklists go... are you required to keep a list of chemicals you store/use on site? If so, that is a place to start. I would even consider using such a list to periodically check if these chemicals have expired, or are even still needed at all, are stored properly etc. That is a big effort too, but it can occasionally be worthwhile. I would not feel the need to use anything more elaborate than a matrix that lists the chemicals, and has boxes to indicate with X the found acceptable criteria. For those that do not conform, I would indicate with a circled 1, 2, 3 etc. and indicate the meaning of these at the bottom of the page. Simple methods are good for a job like this.
I hope this helps!