I have a senior level course that is pretty much dedicated to organometallic chemistry, so it is somewhat challenging for me to think of what I would do in only 5 or 6 classes. But I'll give it a shot. And I apologize in advance for what I feel like is going to be too much self-promotion. I have been working on a bunch of Lit. Discussion LOs lately and while I haven't had this question in mind in developing them, I have had a related question, "what fundamentals of organometallic chemistry can I extract from this paper?" So, I think I can answer your question nicely with Lit. Discussions.

Counting electrons is obviously significant, so I want to make sure that is a part of as many LOs as possible.

First up would be the Lit. Discussion on the Monsanto Acetic Acid Process. Yes, it is an old paper. That's ok. It is very short and something I think students can handle. It provides an opportunity to talk about how carbonyl ligands bond and the concept of back-donation. With that is some discussion of IR characterizaton (and even some group theory if you have covered that earlier in the course). It covers oxidative addition/reductive elimination and carbonyl insertion reactions. It introduces a catalytic cycle. There's also plenty of electron counting. 

My second choice would be Ligand Effects in Titration Calorimetry from the Angelici Lab. I am really showing bias on this one. This is going to build quite a bit on the last LO. There's still lots of electron counting to do. The focus is still on oxidative addition and there are still carbonyls. But we know get to look at the bonding of Cp ligands and how the electron donor ability of Cp compares to Cp*. We also get to examine the electron donating ability of phosphine ligands. There is some simple IR characterization of the carbonyls but also NMR, both ¹H and ³¹P, in particular, the ¹H NMR of metal hydrides. 

Third on the list would be Ethylene Compounds of the Coinage Metals. Once again, we have some electron counting of different ligands. The bonding of ethylene ligands is an important part of this LO. So is the NMR characterization of the compounds and an examination of the X-ray structures. 

Fourth would be Methane Activation by a Tungsten Allyl . This covers the bonding of two other types of ligands, NO and allyl. It is in the context of a current problem of great interest to the field, methane activation. As part of that, the C-H activation reaction is covered. There's lots of great NMR characterization as well as some IR. And there is lots of electron counting practice to be had. 

Lastly (because I need to leave you a lecture on counting) would be Understanding the Mechanism of Grubbs Catalyzed Olefin Metathesis. It's got electron counting. It has carbenes. It has a catalytic mechanism and the topic is olefin metathesis. And even better, it is an LO I didn't write so I can feel a little better about not completely self-promoting through this entire response. 

There you have it. You can't cover everything in 5 or 6 lectures. But you shouldn't feel like you have to. I think this would give great exposure to the field ranging from classic papers to a paper published this year (2017). I am sure my list is missing something and it is very biased by LOs I am very familiar with since I have been working on them recently. There are certainly going to be better LOs that cover these topics. There are also going to be better opinions as to what should or shouldn't be covered. 

Coord Chem and OM kind of go hand and hand in my view. I teach descriptive coord chem and electron counting early in the quarter, then get to OM chem later in the quarter.

I only get about 4-5 days to cover coordination chem and then OM chem in my inorganic class total, and here's what I want students to be able to do:

-Identify X and L-type ligands (and kappa, eta, and mu nomenclature for all ligands)

-oxidation state, d-electron count, and 18-electron counting (I use the "ionic method", basically CBC... the covalent method is whacky)

-HS/LS, paramagnetic/diamagnetic, spectrochemical series/CFT

-Organometallic pi ligands (Frost diagrams, orbital interactions between the metals and the pi ligand orbitals)

-Differentiate between Fischer and Schrock carbenes (and how to count them as ligands). 

-Understand pi-donor and acceptor effects (back donations from CO's, CN's, etc), and predict differences in C-O stretching in IR due to other metal and other ligand identities. 

-Be able to identify various reactions and tell what happens to oxidation state, d-count, 18-electron rule: OA/RE, ligand association/dissociation, ligand insertion/deinsertion

-Identify olefin metathesis catalysts (Grubbs vs. Schrock) and when/why you can use each. 

-Predict organic products from olefin metathesis

-Analyze a catalytic cycle in terms of the e-counting in the species, the steps, the overall balanced chemical equations, and why the conditions are important (added base to react with HX being generated for cross-coupling, the need for HI in the monstanto process, etc). 

-Understand cases where OA proceeds via SN2 chemistry (and do arrow-pushing)

-Understand how a mechanism could be studied (e.g. excess ligand, changing conditions, etc) on a relatively basic level. We don't have time to cover kinetics/advanced mechanistic chem. 

Basically, I have lots and lots of cases where I ask them about the oxidation state, d-count, and 18-electron count. Those are skills that they really need to get from the course.