Problems with thematic roles
Doing the above questions may have given you an insight into some of the problems involved in assuming a fixed inventory of thematic roles. The motivation for postulating a thematic hierarchy was the existence of cases where it’s fairly easy to decide what role to assign arguments to. In John [Agent] kills Mary [Theme], for instance, the identity of the roles couldn’t be more obvious. But there are many occasions where things are much less clear cut, and where we could assign an argument to several thematic roles. In (11), for example, the subject could be analysed as both Agent (initiator of the action) and Theme (entity undergoing motion):

In response to data like these, some researchers have suggested that nouns may instantiate two thematic roles simultaneously (see Jackendoff 1990).
The arguments of many verbs seem hard to assign to any of the conventional thematic roles. For example, it’s not obvious how we should label the roles associated with the following clauses:

In none of these cases is it obvious that the arguments can be assimilated into any of the basic roles. One could, of course, invent new roles for each of the verbs individually, but this tactic would threaten the strength of the original proposal: if our aim is to account economically for the observed general patterns of argument structure, we can’t just invent new roles every time the system breaks down – this would risk exploding the number of roles beyond what investigators have assumed to be reasonable boundaries. Dowty (1991: 561) puts the problem like this:
[t]he variety of semantic distinctions that correlate with syntactic and lexical patterns in one way or another is surely enormous. To postulate thematic role types for each of them is, quite possibly, to dilute the notion beyond its usefulness, but what we lack is a principled way to decide what kind of data motivates a thematic role type
. Even if these problems are resolved, the difficulties are not over. Not only has it not been possible to unambiguously assign arguments to thematic roles, but the thematic hierarchy ranking these roles has proven extraordinarily elusive. Cross-linguistic investigation over a long period has failed to produce any version of the hierarchy on which investigators can agree, since the rankings between different arguments seem to vary consider ably from one language to the next. This in itself is reason to be sceptical of the very idea that Universal Grammar (UG) specifies a thematic hierarchy. As Newmeyer says, ‘[t]here is reason for strong doubt that there exists a Thematic Hierarchy provided by UG. That seems to be the best explanation for the fact that after over three decades of investigation, nobody has proposed a hierarchy of theta-roles that comes close to working’ (Newmeyer 2002: 65). This has certainly not been helped by the fact that different investigators have applied thematic role terms inconsistently. But the problems of reconciling conflicting theta hierarchies is more than simply terminological. Two authoritative investigators, in fact, go so far as to claim that it is simply ‘impossible to formulate a thematic hierarchy which will capture all generalizations involving the realization of arguments in terms of their semantic roles’ (Levin and Hovav 2005: 183).
But even if there were a cross-linguistically accepted thematic hierarchy, cases still exist which call into question its ability to explain argument structure. So-called symmetrical predicates – equal, be similar to, be near, resemble, weigh as much as – show that the thematic hierarchy isn’t the only determinant of argument selection, since the two arguments of these verbs, by definition, share an identical thematic role (see Dowty 1991: 556 for discussion). Something determines the choice between subject and object – just not thematic role. But if thematic role doesn’t deter mine subject-selection in these cases, perhaps it never does.
Now consider the following pair:

The book presumably instantiates the role of theme; Mary is less clear, but perhaps beneficiary is the most appropriate label. In any case, own and belong show a contradictory ranking of arguments. In cases like this, the thematic hierarchy predicts the correct subject–object choice for only one of the verbs. For the other, there must be some other explanation.
Examples like (14), from Italian, pose a similar problem. Here we find experiencer and theme roles being differentially assigned to subject and object position:

This sort of phenomenon is widespread cross-linguistically. English is actually rather lacking here, but the pairs in (15) show the same flipping of thematic roles:

These sentences represent different linguistic construals of the same (or at least a highly similar) situation, one of which is in accordance with the thematic hierarchy, and one not. The verbs in the left column, whose arguments obey the hierarchy, are unproblematic: the grammar does not need to include any special information about how these verbs’ arguments are linked to subject and object, since this is explained by general principles. But the badly behaved cases on the right are different: since frighten, please, and their ilk all violate the thematic hierarchy, the learner has to learn the appropriate argument linking patterns for each verb. This means that there are two types of verb in the lexicon: those whose argument-linking properties conform to the thematic hierarchy and don’t need to be separately learned; and those whose arguments don’t observe the hierarchy and so do need to be learned. Given this situation, it might be a simpler solution to say that the verb always individually specifies what arguments are linked to subject and object, and dispense with the thematic hierarchy altogether as a component of the grammar.
Supporters of the hierarchy could answer here that doing this would ignore a significant generalization: the arguments of most verbs are assigned to subject and object position in accordance with the hierarchy. It’s only exceptional ones like those in (15) which show an option. Furthermore, these verbs are a coherent cross-linguistic class. It’s not just any verb and argument combinations which exist in the pairs like those above. Instead, the choice between two alternants seems mainly to be available for psych-verbs, i.e precisely those verbs which subcategorize experiencer and theme. Other verbs mostly don’t show alternants in which the arguments are flipped: as observed by Carter, there is no English verb *benter which has the same meaning as enter, except that the agent and goal arguments are swapped (*The room bentered John.) The fact that alternants which violate the thematic hierarchy are the exception rather than the rule means that the best policy is to allow the exceptions’ argument linking to be part of the information included in each verb’s lexical entry, leaving the thematic hierarchy to determine all the rest. Proponents of the hierarchy could also point to the fact that its usefulness in the grammar is not confined to solving the linking problem: as noted by Newmeyer (2002), thematic role hierarchies have also been appealed to as the explanation of a range of other grammatical phenomena (e.g. ante cedence for reflexivization (Jackendoff 1972) and the choice of controller in embedded infinitivals (Culicover and Jackendoff 2001)). If we need the hierarchy to do other work in the grammar anyway, the motivation for dispensing with it is reduced.
Whether thematic hierarchies should be retained as part of the explanation of linking depends on a number of tricky metatheoretical issues – in other words, issues about the circumstances in which one theoretical explanation should be preferred to another. It’s fair to say that there is rather little consensus on these issues. At the moment, it is simply unclear whether thematic hierarchies are an appropriate device in the grammar.