For example if you agreed to accept a single lot of goods that didn't fully meet the specification, you might provide them with a letter or message accepting that lot without prejudice to the contract. You want that one act to not have any impact on the contract's requirement that the goods other than that lot must meet the contract requirements. You might do that because at times even thought its not perfect it may be usable and some product is better than no product and you might get other concessions to use the product.
In contracts I always include language to the effect that any waiver must be in writing and be signed by the parties to the agreement. Without that language, you can have a waiver of rights by your inaction in not enforcing your rights. You may be estopped (prevented) from asserting those rights. I'm not a big fan of using general statements. I prefer to be more specific about what I’m agreeing to. If I’m going to agree to waive something, in the separate waiver document, I make it clear exactly what that waiver applies to. If you do that right, you don't need to include the language reserving your rights. You would also not be concerned with having that waiver document introduced as evidence. It would already be clear what that waiver applied to. Any argument to expand that would, per the contract, require a separate waiver document signed by the parties.
In their example the individual had included the language in a section about getting notices of delay, as they wanted the notices of delay to not affect their rights. My opinion was that use didn’t provide them with anything. You use the language in trying to protect against a waiver of rights. Receiving a notice of a delay is not agreement consenting to the delay. If I received a notice of a delay I probably would acknowledge the notice and make it clear in that acknowledgement that unless the delay is excusable per the terms of the contract, their responsibility to complete the work on time still remains in effect. That makes it clear that I still retain all rights I have. The only way those rights may be modified is if there is an excusable delay where any changes to the rights would be modified as part of the change order or variation agreeing to the delay and any extension of time.