Okay, just met with another lawyer who immediately said on his own that it's missing the affidavit of witnesses. When I asked why it wasn't needed back in 1984, he said that the court would then usually call on the witnesses to testify that the testator was of sound mind etc. I don't know how it was done; notarized agreements maybe?
Luckily, he seemed to recognize the second signature and took a chance and looked up the name. This person was a lawyer who supposedly registered in 1957! So of course I assumed he died since he's gotta be at least in his mid 80's by now. But then he called the original office and he's still practicing!
The lawyer explained the situation to him and the witness agreed to attest to the signature. So it looks like that's not a hurdle anymore.
But from speaking to two lawyers, it sounds as if the affidavit is a necessary part of the process that would save time and money.
Thanks to all who chimed in.