Is this a sign or symptom of Alzheimer's or just old age?

My mother in law seems to be having more trouble than usual finding a word, For example, she had a piece of fruit on the table and was telling us that the nectarine had too many seeds so beware. The thought was correct - but it was a tangerine. I asked her again thinking I didn't hear her correctly and she repeated it. I asked if she was referring to the tangerine on the table and she gave me a confused look. tried saying the word like she had never heard of a tangerine before - then the light dawned and she agreed.
We are noticing this type of confusion a bit more frequently. Another example was a long conversation with her son arguing where he was born. Finally it dawned on us that she was thinking of where her brother was born, not her son even though she was looking directly at her son.
After this episode I went to the doctor with her. They gave her a simplistic verbal mental status test - like what day is it, when were you born, etc. Of course she passed.
I took her for her flu shot recently \where she had to complete the standard questionnaire. Before turning it in, I reviewed it for her - she had answered several questions wrong.
She has twice now written a check that was to be for $300.00, but it came back because she had written it for $3.00.
She lives with us so we are noticing these things in the course of daily life. Are these signs of Alzheimers? Do I need to become more vigilent? What should I be watching for?
This is really new territory for me. My only experience with this type of behavior was with my grandma when I was about 10. She would go to the bathroom in the backyard (Flashing back to outhouse when she was a kid), hide scissors in her clothes, etc, it scared the daylights out of me. So my reaction to mom in law may be a bit skewed by my experience.
Any whoo - any info would help
Thanks