Does these symptoms suggest an ill fitting crown? (photo)

The gap that you notice, are you referring to a space or opening under the crown, or just that there is a part of your root that is not covered.  The former could be a problem with poor fit, the latter should be inconsequential on the inside of the tooth, and even a preferred way by many dentists who don't want the crown margins under the gums to irritate the gums.
If there was cement left and has now been cleaned off, then the irritation should only be temporary provided you have good oral hygiene and brush your teeth at least three times a day and floss at least once a day.
If you're having pain when you bite, it is more likely that your crown is "hitting too high" and may need some adjustment.  Recommend returning to your dentist to recheck your bite (occlusion).
If you are having "throbbing pain", then you may need a root canal treatment.
Saying all that, many patients have "temporary" discomfort after dentistry and it just needs some time to calm down and go away.  Return to your dentist, let him do whatever he thinks necessary, and then just give it some time to heal.

I would double check the crown to see if the occlusion (bite) needs adjusting. Even a slightly high spot can make a huge difference. A temporary crown is made of a softer material than a permanent porcelain fused to metal one and may actually wear down a little while it's in place. A permanent crown is much harder and needs to be carefully adjusted so that the bite isn't high. The sooner you have it checked the better.

Whenever there is a space or gap between the edge of a crown and unprepared tooth structure, that's an open margin. Open margins are a problem when plaque (which is mostly bacteria) gets into this space. This can cause decay (also known as caries) to occur around or under the crown. There should be a smooth transition and seal between a crown and the surrounding tooth, without any gaps, spaces, grooves or rough areas. A gap between a crown and the gum is not necessarily an open margin. A crown that ends short of the gums can be o.k as long as the edges are closed, meaning no gaps are present.

What you see on the inside is probably the metal edge of the porcelain to metal crown. Most times a permanent crown feels better than a temporary. One thing that could be causing a continuation of the sensitivity is the lower teeth hitting the new crown too hard. Have that checked. An xray will show if the crown fits. If the bite is adjusted, your tooth should feel a little better every day until you don't notice it any more.

A new crown can feel a bit different that the temporary crown. In general, the permanent fitting process should be less irritating overall than the step to prepare the crown. Any new crown can feel tight, or odd for a few days, but in most circumstances it ought to feel good, normal and "disappear" in a few days.

There are a number of issues that can make a new crown feel funny, odd or just off. If the pressure between it and the neighbor teeth is too much, it will feel squeezed between the teeth. This often resolves in a day or two. The most common bother from a new crown is that the bite can be off. The permanent crown has a much more precise and stiff bite as compared to the temporary one. It IS possible that the new crown can wind up with a bite that's too high. This is the most common source of pain or bother with biting or chewing.

If that's the case, then call your dentist and have them look a the evenness of the bite again. It often requires a quick bite adjustment. Then the tooth often settles down very quickly.

There is always a junction where the crown meets the edge of the tooth-hte "margin". In some cases that is made to fit below the edge of the gum-in that case your tongue really wouldn't notice it. In other situations, that junction is above the edge of the gum and your tongue CAN notice it-whether the margin fits tight and correctly, or whether there is a gap and an incorrect fit.

With any new dental work, give it a few days or a week to settle in. Anything that bothers you much beyond that means you need to call your cosmetic dentist. Tell them what's going on. Often it means returning to the office for a follow up. Don't wait too long, you will just keep feeling sore and bothered.

In your case, it's a good sign that your tooth did well with the temporary. That's a good sign that the tooth itself is healthy and in good condition.

I think you are having a combination of issues: the gum will feel better with the extra cement out. It will probably take a few days for the gum to settle down. I suspect that you may also have a bite issue. In your case I do not think waiting will improve it much. Call your dental office on Monday and ask to be seen for a follow up.

Dear Larkin:
Unfortunately, the photos are not close, or clear enough to make a diagnosis.  The only way to properly evaluate the crown is by a physical examination and x-rays.

Nevertheless, there should be no pain or discomfort if the crown fits properly.
The first thing to do is to go to your dentist and express these concerns.  Any professional wants his patients/clients to be happy and recommend his services.  Talk to your dentist and allow him to go good on the service.
If that fails, go to a second opinion from a prosthodontist, which is the expert on this area.
Best of luck,

It sounds like the contact point is too tight. If your having trouble flossing then this could be the problem. We as dentists try to make sure the contact with the teeth on either side isn't too loose, trapping food. If it is too tight, the periodontal ligament, the tiny space between tooth and bone which has nerves throughout, can be compressed, causing pain. I use a Cerec AC machine which is more accurate than traditional means of making crowns. The crowns don't have metal, so they look more natural.