Could you actually get in trouble if you don't stick to the transport and accommodation stated in your visa application?

In China, the EEB (Exit-Entry Bureau) branch of the PSB (Public Security Bureau) works together with local police to keep track of foreigners in the country. When you stay in a hotel, the hotel is required to forward your passport details to the local police. If you stay in a private residence, you are required to register yourself in the household register at the nearest police station.

When your visa expires, the EEB will contact the police where you last registered, and the police will attempt to track you down. At first this is a phone call to your hosts (hotel/owner of the residence), and they will be satisfied at that point if you confirm that you have applied for an extension to your visa (assuming that's what you have actually done, because they will check). Beyond that, I suppose they might come door knocking but I wouldn't want it to get that far.

As I understand it, the purpose of foreigner registration is so that the police can find you whenever they want to. If your travel plans change, all you need to do is update your registration. If you're staying in another hotel, no specific action is required (other than the hotel taking your passport details, which they are required to do). If you're staying privately, update your own registration. As long as you leave before your visa expires, you won't have any trouble with passport control upon leaving the country.

^{(The above is based on personal experience.)}

As a minimum, I am pretty sure that, if found out, you might have trouble getting a visa for the country again next time.

As a next step, if they decide you never intended to stick with the schedule as announced, they could deport you right away.

Depending on the legislation of the country, they could fine/jail you for lying to the respective authority.

All the visa issues are not an exact science unfortunately. In the end, you might land in jail or being deported by one customs officer, and left alone by another with exactly the same situation.

When deviating from your original schedule, the question is more often how well you can explain your situation to the authorities than what you actually did. There is so much personal judgement in the situation that it's really hard to predict what might happen. Of course, there are legal limits in every country as to what they could do to you in an extreme case, but we all know how some countries use the arrest of foreign citizens as a political tool by accusing them of spying (admittedly rather places like Iran and N.Korea).

One of the biggest issues is not if you stayed in one hotel after claiming you would stay in another. The biggest issue is if you are suspected to lie to cover up something else that you did wrong. If you go to a country, change your schedule and leave on time, you are most likely good. If the officer has reason to believe that something fishy is going on from your un-announced travel pattern, they can use that to ask more direct questions about your purpose of stay. And people who plan to overstay their visa or to work illegally are more likely to fail to stick to their travel schedule.

In the end, there is however always the risk that a customs officer makes a judgment and has you temporarily jailed and then deported if they think that you are suspicious enough to not be in their country.

No one checks for what you put in the visa application. The size of the work force they will need is ridiculous. It is just a pure bureaucracy.

I guess that if you are a Tibetan rights activist and they know about you they might check you out a little bit more.