Should I be losing weight every day?

I'm a daily weigher too because I think it keeps me on track. I really watch my sodium intake. If I have a day with really high sodium, I always know the next morning the scale is going to show a gain. Maybe that's the case for you too?

I weigh myself every couple days and always on mondays.

I don't let a couple lbs up or down bother me, some people it does.

You shouldn't worry.

Being under your BMR can hinder weight loss as your body is not getting enough calories to function and you can slow down your metabolism causing you to loose weight much slower. Try changing your goals to 1 pound lost per week and eat all the cals that MFP suggest and you should loose 0.5-1.5 per week, the range is there as everyone's metabolism is different and a lot depends on water retention.

If my daily caloric intake is less than my Basal Metabolic Rate, shouldn't I be losing weight gradually every day?

I've been at this for just over two weeks now and the weight loss has slowed down significantly. I'm fine with that. But this morning I had an increase of about 1.5 lbs which I can't figure out. I didn't record it because I'm hoping it's an anomaly.

I've been sick this past week, so maybe that's throwing things off. It's certainly cut into my ability to exercise.

Unfortunatly the body does not work like a linear equation. Once I got past the initial "shock" weight. I'll go three weeks w/o seeing a change, maybe even gain a little, and then I'll lose 6 lbs in a week. Then some weeks I'll gain as much as 4lbs, and then lose 8 the next. I'm a big dude so most people won't have that wild a swing, but what I'm trying to say is you want to see a gradual trend downward over several weeks.

It's common to reach a plateau when losing weight but don't worry, it usually picks up again.
Weight can vary on a day by day basis so I agree with the above poster that weighing once a week should be suffcient to guage how you're doing.
Don't forget as well, that muscle weighs more than fat, so if you are working out - it can appear that your weight isn't changing much or that you have put on a few pounds but it is instead more muscle mass that has been produced.

Trust the system. Eat the calories that MFP tells you to eat (inclulding your exercise calories!!!) and you will notice loss. Try, if you can, to only weigh once a week at the same time. I know it's tempting to see progress but with water retention and other things the daily fluctuations can be enough to drive one crazy.

One thing I noticed on your diary;

1. You're severely limiting your calories;
2. Your breakfast is practically non-existent
3. You only eat 3 times a day

To help with cravings and also to keep your metabolism fired, you need to eat a minimum of 5 times a day, 6 would be better. Every 2.5 to 3.5 hours. Look at my diary from yesterday as an example;
http://www.myfitnesspal.com/food/diary/RVachon71?date=2010-01-20 or any other day previous.

I've actually noticed this on alot of peoples food diaries.

lose 10 pounds in a month is certainly possible, especially with a trainer, but not easy. Remember the formula is 3500 calories down will lose you 1 pound... this includes both training (additional calories burned) and eating. So if you want to lose that kind of weight, doing the math you need to either excerise off or eat 8000 calories less per week. That's quite a few; especially when your intake was probably somewhere between 1800 and 2000 before.

Odds are if you're at the weight you're at, you probably have been taking in far more calories than you think. A safe rule of math, btw; is you should never really take in less calories than your body weight (in lbs) X 10 over an extended period; and really X 11 is about right (X15 would be your standard "break even", so if you weigh close to 140 at this point you could eat ~2000 calories per day and be semi-active and maintain your weight).

This is where this is tool is truly starting to help me. I realized I had been taking in ~3400 calories, which is why (similar to you) I had gained about 12 pounds over the last year and a half (since my workout partner had a baby and stopped working out with me). I also hadn't been working out enough. I also got an addiction to sugary beverages (specifically Starbucks Frappucino's and Fat Free Whip Free Rasberry Mochas... 200 calories per drink X ~4 a day adds up), and I randomly snacked a good bit.

Being consious of what you eat is a GREAT start. Cardio should be the crux of your focus but don't forget the muscle work (if you have a good trainer they'll take care of all of this for you, but the bottom line is if you cut that many calories and don't do serious muscle work, you'll burn your muscle frame and weigh less but still not look any better).

Whew! Just some advice; while I've only been "back on dieting" for a week (I look good, but a little bit is "starting to form" on my tummy area, and I don't want it to expand. Plus I got in a bet with some friends ), I've previously had two other phases (one about 12 years ago when I lost 50 pounds, and one 3 years ago when I lost 20; every now and again I just "slip" and have to get refocused). On this week I'm already down 4 pounds. There is straight science and math in losing weight; don't fall for some of the fad diets people want to do, shortcuts never work for anything in life. Just eat healthy, track your calories on here, and work well with your trainer, and you'll hit your goals.

Good luck .

"diet to lose weight":http://www.youtube.com/watch?v=iflCqbDMSMY
"lose weight in 2 weeks":http://www.youtube.com/watch?v=iflCqbDMSMY