监督 vs. 监视
jiāndū vs. jiānshì

监督 indicates “supervision, inspection, such as that of the superior to the subordinate, voters to the representatives, public opinion to officials, people to the government.” 监督 is usually open. It can be the predicate and also the subject, object and attributive.
监视 means “to keep a close watch, e.g. on one’s enemy, or on police suspects, etc.” 监视 is mostly secrative. Besides being an adverbial, it can also function as other sentence elements.

The object of 监督 can be a person or action, while the object of 监视 can be a person, an action or a place. The purpose of 监督 is to promote; while the purpose of 监视 is to discover and guard against activities illegal or harmful to oneself.
(1) 有关部门决定要在节日期间加强价格监督检查。
(2) 舆论可以对干部的行为起到监督的作用。
(3) 他奉命去监视疑犯的一举一动。
(4) 这片区域已经处于我军的严密监视之下。

The two words are not interchangeable.

“监督”表示考察、察看、督促，如官员、人民对政府的监督。监督常是公开的。它可以做谓语，也可以做主语、宾语以及定语。 “监视”表示从旁密切注视并察看，如己方对地方、警察对嫌疑犯，监视常常是隐蔽的。除了状语之外，它还可以充当句子的其他成分。
“监督”的宾语可以是人或活动；“监视”的宾语是也可以是人或活动，还可以是处所。
“监督”的有督促使其朝好的方向发展的意思；“监视”则侧重于发现和防范违法的或不利于自己的活动等。
两个词不能互换。