Hi,
1) Does a mere promise itself create a contractual obligation?

2) if or both parties to a contract enter into it under some misunderstanding or misapprehension, in what circumstances will they be permitted to allege that the contract is defective, on the ground that, if they had known the true facts, they would never entered into the agreement?

#1.
In most states, a verbal contract is a legal and binding contract. The problem is that if it went to court, it would all be up to what the judge or jury came down to believing the original agreement was... which, of course, would be difficult since the parties will be giving different stories of what it was and how it was to be enforced.

#2.
This one makes it far, far more difficult. Without certain details in writing, then the whole thing gets left up to someone else (judge or jury) if it goes to court.

Without knowing the details, I can only suggest to put on your best tact and diplomacy and try to work it out with the other party.

Here's something to think about too:

I can guess one of the parties wants more money or services and the other is happy to walk away. Is that right?

If so, then it will be up to the party that wants more to pursue it... which will cost a lot of money or time.

With regard to your first question, in order for there to be a contract then some consideration must be given. Consideration is usually in the form of money but it can also be a promise as well. For example, you may make a promise to me that you will give me a deed for your house and property. But unless I give you money in return for that promise, or unless I make a promise to you that has some kind of value to you, such as a promise that I will give you a deed for my house and property in return for your promise, then there is no contract. Consideration can be a complex issue and there have been many lawsuits over what exactly constitutes sufficient consideration to create a contract. Check out http://en.wikipedia.org/wiki/Consideration for more information.

With regard to your second question, you are talking about a combination of two things: a failure to have a meeting of the minds, and the parol evidence rule. If there is no meeting of the minds, where both parties understand and agree about the contents of the contract, then the contract is void. In order to determine whether there has been a meeting of the minds it will be necessary for the parties to give parol evidence, which is evidence concerning the contents of a contract that is not already contained within the terms of the written agreement. The situations when parol evidence may be given to modify or terminate a contract are also complex and there have been many lawsuits about this situation as well. Check out http://en.wikipedia.org/wiki/Parol_evidence_rule for more information.

In regards to your second question, isn't this how Arnold S. got the process going so he could be elected as California's governor?

Uh, folks, I think we just did some homework for someone here, just a wild guess. :(
But the one about the California Gov. was a good one, I liked that. Lets just hope the constitution does not get changed for the next 100 years...