I don't know who first thought this idea up, but Orin Kerr seems to name it in this law review article. He describes it as law enforcement doing every search or seizure step constitutionally and the result as a whole still being unconstitutional. This would be a departure from the normal mode of search and seizure analysis because in the normal mode if every search or seizure step is constitutional the result as a whole is constitutional. It is worth noting that the mosaic theory is not a theory which has roots in a controlling Supreme Court decision.
The best way that I have come up with to describe the current method of constitutional analysis is a simple mathematical equation. Every search or seizure in the entire equation is assigned a "1" if constitutional or a "0" if unconstitutional. The equation proceeds as follows.
1 X 1 X 1 X 1 X 1 X 1 X 1 = 1 (Constitutional)
1 X 1 X 0 X 1 X 1 X 1 X 1 = 0 (Unconstitutional)
If every one of the searches and seizures is constitutional, then the entirety is constitutional. If any one of the searches or seizures is unconstitutional, then the entirety is unconstitutional. It is a straight forward, rational way to approach constitutionality. Obviously, the proposed "mosaic theory", as presented, fails to model in this manner because it would look like this.
1 X 1 X 1 X 1 X 1 X 1 X 1 = 0 (Constitutional = Unconstitutional)
The mosaic theory is really nothing new. It's aggregation as constitutional violation. As such, it is a subset of an individual constitutional test. Anyone who has argued the constitutionality of a traffic stop has dealt with this. A traffic stop which is constitutionally valid can be made unconstitutional if it is extended beyond a reasonable time to accomplish its initial purpose. This is an aggregation of time and it is similar to the aggregation of time which is pointed to in the Jones concurrences and is cited as a basis for the mosaic theory. In that case, the concurrence would have allowed initial placement of the gps tracker but ruled it unconstitutional after a certain amount of time had aggregated.
What both the traffic stop and the Jones concurrences point to is the fact that there are a number of factors in each of the search and seizure events which comprise the entirety. In other words, the model is actually something like this:
(1 X 1 X 1) X (1 X 1 X 1 X 1) X (1 X 1 X 1) = 1
(1 X 1 X 0) X (1 X 1 X 1 X 1) X (1 X 1 X 1) = 0
(A) X (B) X (C) = ENTIRETY
Applying this to a traffic stop, we'll say A is the seizure of the vehicle and its passengers, B is the search of the vehicle, and C is the search of the driver's person. Since everything in B and C is fine we'll concentrate on A. Let's say the sub-elements in A are (1) reason for stop, (2) behavior during the stop, and (3) length of the stop. The reason for the stop is valid (speeding). The officer's behavior during the stop is polite and concentrates on the ticket. In the first model the officer releases the car and driver after a 15 minute stop. In the second model the officer sits in his car with the driver's license for 55 minutes until a drug dog shows up and is run past the vehicle (40 minutes longer than the ticketing process takes). This aggregation of time is unconstitutional and therefore the seizure of the vehicle and passengers is unconstitutional and therefore the ENTIRETY is unconstitutional.
To be clear, aggregation does not have to be about time. In U.S. v. Edwards the 4th Circuit ruled a search unconstitutional not because the search was without constitutional basis, but because of the aggregated factors of the locale where the search was done and the manner in which it was carried out.
The mosaic theorists claim the aggregation as the entirety and in one sense they are right. It is the entirety in that if it fails the entirety fails too. However, this is true of every constitutionally significant issue and sub-element of that issue. Stating that one sub-element is the whole is nonsensical. To consider it in reverse, if the traffic stop does not aggregate to the point that the seizure of the vehicle and passengers is unconstitutional and therefore A=1, this does not mean that B=1 or C=1.
The mosaic theory is badly flawed. However, aggregation analysis will become more and more important in the modern world. To base 4th Amendment analysis on whether something can be viewed by the world at large is becoming an increasingly poor way to frame things in a world where the phone in your pocket identifies where you are 24 hours a day, your ISP can track your internet activity, and you are required by law to hand over information about yourself to the government and private industry. Unless courts are going to find that the putative "reasonable person" is a guy living in a cabin in the Rockies hand typing his libertarian manifesto, in short order any "reasonable person" will be observable for the vast majority of his life. We must adjust; we just need a better model than the mosaic theory.