I already have a table of TMM normalised RNA-seq values, but do not have access to the raw reads. Is it possible to do an MDS plot and calculate the common dispersion, and then do a differential gene expression? I have tried using edgeR to read the normalised values into a $counts table of a DGEList, but have not had much success. Estimating the common dispersion creates an error.

What do you mean by "TMM normalized" RNA-seq values?

Is this the equivalent of calling cpm(calcNormFactors(y)), where y would be the DGEList (with counts) object that you wish you had right now?

If this is the case, I'd log2 transform these and pass through eBayes(..., trend=TRUE).

Assuming your.data is the matrix of cpm values and you have 3 replicates per sample, that would look something like this:

## first filter your data to remove lowly expressed genes
filtered <- rowSums(your.data > 1) >= 3
dat <- log2(filtered + small.prior.count.if.you.have.0s)
fit <- eBayes(lmFit(dat, design), trend=TRUE)
res <- topTable(fit, ...)

Refer to this thread for more information:

A: What was the very first paper to describe "limma-trend"?