It appears that Zebest has some experience with Illustrator and Photoshop, but none at all with Acrobat. She commits a very basic error throughout her document - she seems to be completely unaware that the White House copy of Obama's birth certificate is a compressed image. Why is this important? Because nearly all of her "suspicions" are easily explained as compression artifacts.
A real quick background on PDF compression - there are two main compression schemes in use here: JPEG and JBIG. JPEG is a compression scheme for color images that utilizes combinations of LZW (Lempel Ziv Welch), frequency analysis and DCT (Discrete Cosine Transform) to achieve impressively high compression. The JPEG compression scheme is lossy - meaning that some information will be sacrificed in order to achieve higher compression ratios.
JBIG is a compression scheme designed for bi-level (monochrome) images. It makes use of image segmentation, meaning that it can apply different compression algorithms to different parts of the image.
The exact routes followed by the image compressor very from vendor to vendor. This particular PDF was apparently created on a Mac using software not written by Adobe. Since the encoder algorithms are proprietary information, we can only talk about the compression process in general terms.
The first step is to separate the color components of the image from the monochrome components. Obviously, the green background will form most of this layer. However, it appears that some of the text was also assigned to this layer - probably due to the fact that the text color tends to vary throughout the document. The lighter elements (such as the 'R' in Barack) were recognized as color and assigned to the bottom layer.
The monochrome layer is then further split into constituent elements. The encoder will attempt to separate text, line art and general raster (bitmap) data from the image. Again, we don't have access to the compression algorithm, so we cannot say for sure how the separation was done.
The separated images are then subjected to a pattern matching algorithm that attempts to find duplicates. The reason behind this is that it is far more efficient to represent several images using one symbol. The exact threshold at which the encoder decides that two sub-images are the same is unknown.
When we look at all of these elements together, we can make a few guesses about what sort of artifacts we would expect in the PDF. First, we note that it is quite possible that parts of the text may be represented by different encoding schemes. In figure 5, for example, Zebest points out that the '4' and the '1' in the serial number appear to be different. Zebest is here comparing apples and oranges - the '1' was assigned to the color layer, and is encoded using a multi-bit color mapping, while the '4' was compressed with JBIG, and is thus monochrome. The 'noise' that Zebest is talking about exists only in her mind.
We would also expect that some symbols would be repeated. In figure 6, she notes that the 'i' is identical despite appearing in two different places. As we have seen, this is due to the compression algorithm deciding that they are similar enough to represent with the same symbol. This phenomenon occurs quite frequently in the compressed image - even the '1st' and '2nd' checkboxes in section 4 of the document were replaced with the same symbol, but the '3rd' was not. This strongly indicates that the duplicate detection was done via software rather than a human agency.
In short, by being ignorant of the manner in which image compression works in PDFs, Zebest's analysis is completely useless. Most of her points are irrelevant, and thus the "forgery" accusation remains unproven.