Other concerns

Other concerns
Besides a criminal record, CIC lists a host of other situations that may prevent admission into Canada. While most of these shouldn't be an issue for the average traveler (e.g. previously overstayed or violated visa conditions, human rights violations, involvement with terrorism or organized crime, etc...), there are a few that do occasionally complicate or bar entry for visitors:
Purpose of visit. The days when you could simply walk over the Rainbow Bridge with your driver's license, telling customs that you wanted to see the other side of the city are long gone. If you're visiting as a tourist (including day-trip pedestrians from Niagara Falls, NY or Detroit), border officers are going to want a detailed itinerary of the places you'll be visiting. It's a good idea to have this information written down ahead of time, and to include contact information if any of your destinations aren't standard tourist attractions or more off the beaten path. Also be prepared with a physical street address at which you will be staying (a hotel name by itself is not acceptable) if you'll be in the country for more than a single day.
Letter of invitation. In absence of a visa authorizing employment, long-term residency or study, a letter of invitation (sometimes called a "letter of introduction") is required for persons visiting for any reason other than tourism (including visiting relatives or friends). For business visitors, there is specific information this letter must contain (including a statement of financial support), but for everybody else something in writing (e-mail or hard copy) along with contact information from the person you're visiting is sufficient. You must bring the letter with you to the port of entry, even if you used it to apply for a temporary resident visa. The letter of invitation requirement is strictly enforced. If you are a business visitor and show up without one you will be denied entry. Others may or may not be admitted after significant delays and additional rounds of unpleasant questioning while border officials attempt to verify your story.
Health concerns. If you are very sick, to the point where the border officer has to consider whether you might burden the healthcare system during your visit, you will be denied entry.
Support funds . You need to prove you have enough funds to support yourself and dependents while in Canada. For most Western tourists a major credit card (not a debit, ATM or bank card) is sufficient.
Inadmissible family members. If you have an immediate family member who is deemed inadmissible, you may also be disqualified from entry based on that fact, although this is at the discretion of the border or visa officer. It seems to be a problem more for persons with known terrorists, members of the Mafia, or other high profile criminals in their family, not just a sibling with a misdemeanor conviction.
As a general rule, admissibility and rehabilitation decisions cannot be appealed beyond a supervisory review at the visa office or border. The only exception is if you can prove the decision was based on wrong information (for example you were acquitted of a crime, but that fact was never properly recorded in Canada's database.) That being said, you are usually allowed to apply again once any specific issues relating to a refusal have been corrected, once the requisite time has passed for rehabilitation, or one year after being denied rehabilitation.