This is a great question that many people wish for an answer. However, I think there are a number of reasons why phylogenetic incongruence between trees built from morphological vs molecular data can occur. One obvious reason that may create conflicting trees is that the morphological data may include noisy or homoplasious characters due to a) convergent evolution, b) misidentified character states, c) morphological variation across character states imposed by environmental variation impacting on plastic morphological traits, with such variation interpreted as binary, d) improper weighting or ordering of character states, etc. On the molecular side, incongruence can happen due to a) phylogenetic noise in the data, b) weak phylogenetic signal, c) impact of positive or selective sweeps across the gene of use, d) incomplete lineage sorting, e) paralogy issues, f) recombination, g) hybridization, h) molecular saturation at sites (noise), and a number of other issues. These lists are certainly no exhaustive. The challenge becomes trying to determine which of these conflict creators are at play.
To be honest, this question is not really addressable without sounding very negative about the traditional approaches in plant taxonomy. Actually, the waste majority of so-called conflicts between morphology and molecular data are not conflicts between data at all! It is rather common that these conflicts turned out to be a conflict between what the information provided morphological data actually provide and the perception (and often misleading) interpretation of some researchers. This is mostly caused by the application of inappropriate arguments/ hypotheses about the evolution of morphological characters which result incorrect homology assessments, inappropriate polarisation of character evolution and unnatural classifications to name on some. Of course, as evolutionary biologist and taxonomists we have to take into account complex modes of evolution which create sometimes conflicts between the hypotheses obtained by the analyses of different datasets. However, this is not a conflict between morphological and molecules. The early days of the phylogenetic revolution have shown this again and again and I am a bit shocked that this notion - molecular versus morphological - has not been recognised as what it is .. a phenomenon interested to researchers studying the history of sciences that lacks any proper scientific support as it was worded. We need to move forward and look carefully about conflicting information that can be traced in phenotypes and genotypes .. and any phenotypic trait will have its genotypic blueprint. Thus, we can not have a conflict between morphology and molecules because genotype and phenotype are tightly linked. All reasons for conflicts mentioned in the discussion above are caused by conflicts traceable in the genomic data. However, I am afraid some people still do not appreciate sufficiently the evolutionary continuity of genotypes and phenotypes. A small study published some years ago may help you to get a bit more information on this: Schneider et al. 2009 Systematics Botany.
I appreciate Dr. Schneider's response. Although it is absolutely correct that phenotype and genotype are lightly linked, I would add that the link between phenotype and genotype can sometimes be obscured and is not always one-to-one. Many traits are quantitatively controlled and thus result from the interactions of multiple genes. Unless this genetic control mechanism is understood, there may be some discordance between morphology and molecules. Another example is when a phenotype is impacted by epigenetic mechanisms. I absolutely agree that genotype and phenotype are tightly linked, but I think the discordance can come in when these links are not fully understood or when phenotype is coded without complete knowledge of the genetic control (which is most of the time the case). And, like Dr Schneider states, when these instances of discordance occur -- it presents a wonderful opportunity for investigation.