Well, Friedrich III had more liberal leanings than his father or his son, but contrary to AH-legend, that doesn't make him a true-blood liberal which turns das Deutsche Reich into a continental Great Britain.
Also, he wouldn't be powerful enough to undertake any radical steps which would run completely contrary against the German mood of the time.
For example, I cannot see this experienced commander of German forces break the militarism in German society.
Also, he would probably not change the constitution. First of all, the 1871-constitution was rather progressive (especially the franchise) and still brand-new in '78. He might do something about the franchise in the state of Prussia which was centered around a census-system, but I am not sure if that was an issue in the 1870s already as it was in the early 20th century.
Friedrich III might replace Bismarck by chancellors which can rely on a majority in the Reichstag, but in the case of a successful assassination of Wilhelm I by a political radical, we might see even harsher "Sozialistengesetze" and ironically a worse internal climate in the years to come. Also, without Bismarck, Germany might not see the series of social insurances he introduced.
What we could expect for the time being would be excellent German-English relations. However, at this point of time there is not a chance of a developing alliance due to Britain not being interested and Friedrich's successor would still have plenty of time to ruin the relationship.
On the other hand, a liberal emperor who antagonizes Russia might lead to an earlier end of French isolation...and here things become interesting.