There will be an adjustment period of up to six months as the dog gets situated in his new digs. Many dogs coming out of shelters have been abused or neglected and haven't had the benefit of living in a good home. Dogs love structure and consistency, which is why it is important to begin training right off the bat. Set the boundaries in the home and outside especially if you're living in an urban environment where there is a lot of external stimuli.
Teach the dog not to jump on counters when food is being prepared, not to jump on beds or couches without your permission, how to sit before eating a meal, how to walk properly on leash etc. If you see a pattern of negative behaviors don't just return the dog to the shelter, hire a trainer. The majority of behavioral issues can be overcome with training and patience.