A gist to show off my problematic FBO copy code. The copy method creates a dynamic texture and then tries to copy it to the destination texture. The result is always that the destination becomes entirely filled with whatever pixel is at texture coordinate (0, 0) on the input texture. This code runs fine without GL errors of any kind on a Galaxy …

FBO Copy Method

  public void UpdateTexture(float value) {
		checkGlError("pre-UpdateTexture");

		// Save the current state
		IntBuffer previousFBO = IntBuffer.allocate(1);
		IntBuffer previousRenderBuffer = IntBuffer.allocate(1);
		IntBuffer previous_program = IntBuffer.allocate(1);
		GLES20.glGetIntegerv(GLES20.GL_FRAMEBUFFER_BINDING, previousFBO);
		GLES20.glGetIntegerv(GLES20.GL_RENDERBUFFER_BINDING,
				previousRenderBuffer);
		GLES20.glGetIntegerv(GLES20.GL_CURRENT_PROGRAM, previous_program);

		// Need to set up the FBO first
		if (mFrameBuffer <= 0) {
			Log.w(TAG, "ERROR FBO not created");
			return;
		}

		// Generate a new image and update source texture
		this.generateImage(value);

		// Set up our FBO
		GLES20.glBindFramebuffer(GLES20.GL_FRAMEBUFFER, mFrameBuffer);
		checkGlError("glBindFramebuffer");
		GLES20.glViewport(0, 0, TEXTURE_WIDTH*4, TEXTURE_HEIGHT*4);
		checkGlError("glViewport");
		GLES20.glDisable(GLES20.GL_BLEND);
		GLES20.glDisable(GLES20.GL_DEPTH_TEST);
		GLES20.glDepthMask(false);
		GLES20.glDisable(GLES20.GL_CULL_FACE);
		GLES20.glBindBuffer(GLES20.GL_ARRAY_BUFFER, 0);
		GLES20.glBindBuffer(GLES20.GL_ELEMENT_ARRAY_BUFFER, 0);
		GLES20.glPolygonOffset(0.0f, 0.0f);
		GLES20.glDisable(GLES20.GL_POLYGON_OFFSET_FILL);
		checkGlError("fbo setup");

		// Load the shaders if we have not done so
		if (mProgram <= 0) {
			createProgram();
			Log.i(TAG, "InitializeTexture created program with ID: " + mProgram);
			if (mProgram <= 0)
				Log.e(TAG, "Failed to initialize shaders!");
		}

		// Set up the program
		GLES20.glUseProgram(mProgram);
		checkGlError("glUseProgram");
		GLES20.glUniform1i(mUniforms[UNIFORM_TEXTURE], 0);
		checkGlError("glUniform1i");

		// clear the scene
		GLES20.glClearColor(0.0f,0.0f, 0.1f, 1.0f);
		checkGlError("glClearColor");
		GLES20.glClear(GLES20.GL_COLOR_BUFFER_BIT);

		// Bind out source texture
		GLES20.glActiveTexture(GLES20.GL_TEXTURE0);
		checkGlError("glActiveTexture");
		GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, mSourceTexture);
		checkGlError("glBindTexture");

		GLES20.glFrontFace( GLES20.GL_CW );
		
		// Our object to render
		ByteBuffer imageVerticesBB = ByteBuffer.allocateDirect(8 * 4);
		imageVerticesBB.order(ByteOrder.nativeOrder());
		FloatBuffer imageVertices = imageVerticesBB.asFloatBuffer();

		imageVertices.put(new float[]{
				  -1.0f, -1.0f,
			    1.0f,  -1.0f,
			    -1.0f,  1.0f,
			    1.0f,   1.0f}
		);
		imageVertices.position(0);
		
		// The object's texture coordinates
		ByteBuffer textureCoordinatesBB = ByteBuffer.allocateDirect(8 * 4);
		imageVerticesBB.order(ByteOrder.nativeOrder());
		FloatBuffer textureCoordinates = textureCoordinatesBB.asFloatBuffer();
		
		textureCoordinates.put(new float[]{
				  0.0f, 1.0f,
			    1.0f, 1.0f,
			    0.0f, 0.0f,
			    1.0f, 0.0f}
		);
		textureCoordinates.position(0); 
		
		// Update attribute values.
		GLES20.glEnableVertexAttribArray(ATTRIB_VERTEX);
		GLES20.glVertexAttribPointer(ATTRIB_VERTEX, 2, GLES20.GL_FLOAT, false, 0, imageVertices);
		GLES20.glEnableVertexAttribArray(ATTRIB_TEXTUREPOSITON);
		GLES20.glVertexAttribPointer(ATTRIB_TEXTUREPOSITON, 2, GLES20.GL_FLOAT, false, 0, textureCoordinates);
		// Draw the quad
		GLES20.glDrawArrays(GLES20.GL_TRIANGLE_STRIP, 0, 4);
		
		// Reset everything
		GLES20.glActiveTexture(GLES20.GL_TEXTURE0);
		GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, 0);
		GLES20.glActiveTexture(GLES20.GL_TEXTURE1);
		GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, 0);
		// GLES20.glBindVertexArrayOES(0); //not universally supported, may need
		// to do some device-by-device logic here. see
		// http://stackoverflow.com/questions/14406829/undefined-reference-glbindvertexarrayoes-glgenvertexarraysoes-gldeletevertexarra

		GLES20.glDisableVertexAttribArray(ATTRIB_VERTEX);
		GLES20.glDisableVertexAttribArray(ATTRIB_TEXTUREPOSITON);

		// Restore state
		GLES20.glBindFramebuffer(GLES20.GL_FRAMEBUFFER, previousFBO.get(0));
		GLES20.glClear(0);//I've heard qualcomm devices need this after a glBindFramebuffer
		
		GLES20.glBindRenderbuffer(GLES20.GL_RENDERBUFFER, previousRenderBuffer.get(0));
		GLES20.glUseProgram(previous_program.get(0));
		checkGlError("end update");
	}

FBO Setup

private boolean createFBO() {
		if (mUnityTexture <= 0) {
			Log.w(TAG, "Unity Texture not set");
			return false;
		}

		// Create a new framebuffer if needed
		if (mFrameBuffer <= 0) {
			IntBuffer frameBuffers = IntBuffer.allocate(1);
			GLES20.glGenFramebuffers(1, frameBuffers);
			mFrameBuffer = frameBuffers.get(0);
			checkGlError("glBindFramebuffer");
		}

		// bind FBO
		GLES20.glBindFramebuffer(GLES20.GL_FRAMEBUFFER, mFrameBuffer);
		checkGlError("glBindFramebuffer");
		GLES20.glClear(0);//I've heard qualcomm devices need this after a glBindFramebuffer
		checkGlError("glClear");

		// bind the output texture and attach it
		GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, mUnityTexture);
		checkGlError("glBindTexture");

		GLES20.glTexImage2D(GLES20.GL_TEXTURE_2D, 0, GLES20.GL_RGBA,
				TEXTURE_WIDTH, TEXTURE_HEIGHT, 0, GLES20.GL_RGBA,
				GLES20.GL_UNSIGNED_BYTE, null);

		checkGlError("glTexImage2D");

		GLES20.glTexParameteri(GLES20.GL_TEXTURE_2D, GLES20.GL_TEXTURE_WRAP_S, GLES20.GL_REPEAT);
		GLES20.glTexParameteri(GLES20.GL_TEXTURE_2D, GLES20.GL_TEXTURE_WRAP_T, GLES20.GL_REPEAT);
		GLES20.glTexParameteri(GLES20.GL_TEXTURE_2D, GLES20.GL_TEXTURE_MAG_FILTER, GLES20.GL_LINEAR);
		GLES20.glTexParameteri(GLES20.GL_TEXTURE_2D, GLES20.GL_TEXTURE_MIN_FILTER, GLES20.GL_LINEAR);
		checkGlError("glTexParameteri");

		GLES20.glFramebufferTexture2D(GLES20.GL_FRAMEBUFFER,
				GLES20.GL_COLOR_ATTACHMENT0, GLES20.GL_TEXTURE_2D, 0, 0);
		checkGlError("glFramebufferTexture2D");
		GLES20.glFramebufferTexture2D(GLES20.GL_FRAMEBUFFER,
				GLES20.GL_COLOR_ATTACHMENT0, GLES20.GL_TEXTURE_2D,
				mUnityTexture, 0);
		checkGlError("glFramebufferTexture2D");

		// Did it work?
		int status = GLES20.glCheckFramebufferStatus(GLES20.GL_FRAMEBUFFER);

		if (status != GLES20.GL_FRAMEBUFFER_COMPLETE) {
			Log.w(TAG, "ERROR: UNITY PLUGIN CANNOT MAKE VALID FBO ATTACHMENT FROM UNITY TEXTURE ID");
			return false;
		}

		checkGlError("glCheckFramebufferStatus");

		return true;
	}

Shaders

String vShaderStr = "attribute vec4 position;                   \n"
				+ "attribute mediump vec4 textureCoordinate;            \n"
				+ "varying mediump vec2 coordinate;                     \n"
				+ "void main()                                          \n"
				+ "{                                                    \n"
				+ "  gl_Position = position;                            \n"
				+ "  coordinate = textureCoordinate.xy;                 \n"
				+ "}";

String fShaderStr = "varying highp vec2 coordinate;             \n"
				+ "uniform sampler2D texture;                           \n"
				+ "void main()                                          \n"
				+ "{                                                    \n"
				+ "  gl_FragColor = texture2D(texture, coordinate);     \n"
				+ "}";