Newsflash:
* Interpol does not have legal powers within the US.
* They do not arrest people. Even if they did, the new order would not give them arrest powers within the United States.
Interpol basically acts to maintain databases and facilitate communication between nations for the investigation of international crimes.
The only part of this order that might be remotely troubling is section 2c, which protects Interpol from search and seizure of their assets. (The President, by the way, has the authority to waive this protection.)
Think about this for a minute.
Interpol maintains databases with information from 189 countries.
While American citizens are, and should be, entitled to information held by the US government under the Freedom of Information Act, the same rights do not apply to foreign information. How would you feel if a Russian lawyer was able to petition the FBI for access to its records?
Interpol exists to foster cooperation between law enforcement organizations and make international investigations easier.