We study the spectral and morphological characteristics of the diffuse Galactic emission in the WMAP temperature data using a template-based multilinear regression, and obtain the following results. (1) We confirm previous observations of a bump in the dust-correlated spectrum, consistent with the Draine & Lazarian spinning dust model. (2) We also confirm the "haze" signal in the inner Galaxy, and argue that it does not follow a free-free spectrum as first thought, but instead is synchrotron emission from a hard electron cosmic-ray population. (3) In a departure from previous work, we allow the spectrum of Hα-correlated emission (which is used to trace the free-free component) to float in the fit, and find that it does not follow the expected free-free spectrum. Instead there is a bump near 50 GHz, modifying the spectrum at the 20% level, which we speculate is caused by spinning dust in the warm ionized medium. (4) The derived cross-correlation spectra are not sensitive to the map zero points, but are sensitive to the choice of CMB estimator. In cases where the CMB estimator is derived by minimizing variance of a linear combination of the WMAP bands, we show that a bias proportional to the cross-correlation of each template and the true CMB is always present. This bias can be larger than any of the foreground signals in some bands. (5) Lastly, we consider the frequency coverage and sensitivity of the Planck mission, and suggest linear combination coefficients for the CMB template that will reduce both the statistical and systematic uncertainty in the synchrotron and haze spectra by more than an order of magnitude.