I am building a dining room table and it has taken me several months to cut all the pieces. Will the glue have any problems sticking to the edges that have been jointed/cut several months ago? I am talking about the top in particular.
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Will the glue have any problems sticking to the edges that have been jointed/cut several months ago?
Yes. Joint failures from wood movement can and do happen if older surfaces are glued.
As you're doing a panel glue-up where the glue presumably will have to do all the work (long-grain butt joints) it's critical that you ensure your edges are ready to accept glue for maximum joint strength.
Glue surfaces should be freshly worked as much as possible, within the hour if possible.
While this sounds nearly impossible for the home woodworker older worked surfaces can be made glue-ready, or 'reactivated', with just a little light sanding according to studies done at the Forest Products Laboratory. A couple of passes with med/fine abrasive should usually be sufficient.
Where appropriate, scraping or a very light shaving taken off with a suitable plane can accomplish the same thing.
This is mostly covered in a previous Q&A, What do I need to do to prepare wood for gluing?
There should be no problem with the adhesion of glue to old surfaces (unless they've been weathered or had some other kind of contamination.)
The only issue would be if the wood has moved due to seasonal humidity changes. This could cause the wood to warp (or bow/cup/etc.), causing the joint to no longer align or fit tightly.