The French word problematique simply refers to things that are problematic or troublesome. In terms of literature, it has come to refer to any problems presented that are impossible to look at in isolation because they all build on each other, they are a "system of problems." The term was first used in the context of a system of problems by Hasan Ozbekhan who pointed out the "49 Continuous Critical Problems facing humankind" and stated:
We find it virtually impossible to view them as problems that exist in isolation--or as problems capable of being solved in their own terms ... It is this generalized meta system of problems, which we call the 'problematique' that inheres in our situation. ("Global Problematique").
Since then, others have also used the term to refer to a system of interlocking problems.
In Act 2, Scene 4, one problem causing an interlocking system of problems is that of course Viola has disguised herself as a boy. This problem has also allowed for the occurrence of a second problem, which is of course that she has fallen in love with Duke Orsino while pretending to be his eunuch servant. Working for Orsino as his servant has also opened the door to the third problem that he has become quite fond of her as his servant, so fond that he pours out his heart to her. The problem of his speaking candidly to her as a boy of course presents other problems specific to this scene. For example, Orsino hears Viola as Cesario speak so "masterly" about the beauty of music and music's connection with love that he next feels obliged to ask Cesario if she has ever been in love, as we see in Orsino's lines:
My life upon't, young thou art, thine eye
Hath stay'd upon some favour that it loves:
Hath it not, boy? (II.iv.23-26)
Viola as Cesario is then obliged to speak honestly but in a deceptive manner, saying, "A little, by your favour" (27). Viola uses the term favour with a double meaning here. It can mean "if you please" or it can also mean "face or appearance" (eNotes); hence, in disguise, Viola is really confessing to Orsino that she loves his face, meaning that she loves him, and such a confession could lead to further problems if he should understand her meaning. Hence, we see that the problem of Viola's disguise plus the fact she has fallen in love both combine together with other problems to form one great big problematique.