Is the basic RBC model a weak model? There are a plethora of examples of weaknesses in my textbook, such as:


The Walrasian assumption
Not including nominal shocks
Not including indivisible labour
Not including distortionary taxes
Not including multiple sectors and sector specific shocks


In my opinion the greatest weakness is the Walrasian assumption, as I think this is not too realistic in the real world.

I think we want to measure degree of weakness by how closely we see the results posited by the model exhibited in the real world. 

So if you have read some articles that improve on the basic RBC model, what are the common extensions (1-5, or other) that you see that address these weaknesses?
When is a model really weak?

A model is an abstraction of reality, to explain a part of it. A model is weak when it cannot explain what it's supposed to be explaining. Just adding features to a model has no intrinsic good. It's much different from a fruit salad, where usually, an increased variety in fruits will lead to a better taste. Here, adding more features makes it hard to understand which feature of the model was necessary to generate the result observed.

For example, When your focus is on variation of labor-supply within different income and skill groups, yes, lack of distortionary taxes could be a problem. If the model is not aimed at doing that, and it does fulfill its purpose without requiring those taxes, the lack therein is not a problem.

The most basic RBC model

There is no single RBC model. It's most simple (but not representative!) version is the seminal Kydland and Prescott (1982) paper. It lacks all those features that you mention, but it is aimed at explaining variations and correlations in output, investment, capital and labor. If it does that job well (I'm not going into that discussion here), it is a good model, and the lack of those characteristics is not a weakness.

The class of RBC models

The general RBC class of models are those, where variation along the balanced growth path is caused by (random) shocks to productivity. Of course, no economist really believes that a random number generator is attached to each firm and causes fluctuations in output. It's a simplification.

Hence, if you are after a weakness behind the RBC model in general, it ought to be that you believe that this simplification is false. That, whatever the reason for business cycle fluctuations we observe is not caused at the productivity wedge. 

For example, some neokeynesian economists believe that it could be mood shocks. People sometimes are more or less lazy, and that recessions go really bad when you people really don't want to work (again, this is a simplification, but the point is that the relevant wedge is not at the output margin, but at the labor-supply and consumption wedge). A critique of these shocks to the household's objective function can be found in Chari, Kehoe, McGratten (2009).

These productivity shocks are, in the simple one-sector model that is mostly used isomorphic to shocks to technology. However, this doesn't mean that they necessarily are caused by them (hint at @Mustang). For example, Acemoglu and coauthors (2012) show how mathematically small shocks within firms and sectors (such as variations in the cost function, e.g. unexpected oil price changes), usually cancel each other out, but sometimes aggregate up to great shocks over the whole economy.